#BEGIN OUTFILE1 # Begin Function number 3 display_alot := proc(iter) global DEBUGL, ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_iolevel, #Top Generate Globals Decl glob_iter, glob_current_iter, glob_start, glob_large_float, glob_hmin, hours_in_day, glob_max_opt_iter, glob_html_log, glob_orig_start_sec, glob_smallish_float, glob_no_eqs, glob_max_order, glob_log10_abserr, glob_log10normmin, glob_percent_done, glob_normmax, glob_reached_optimal_h, glob_dump, glob_max_hours, glob_hmin_init, glob_not_yet_finished, glob_almost_1, years_in_century, glob_optimal_expect_sec, glob_log10abserr, glob_warned, glob_log10_relerr, glob_hmax, glob_disp_incr, glob_optimal_done, glob_initial_pass, glob_display_flag, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_h, glob_clock_start_sec, djd_debug2, djd_debug, glob_max_minutes, glob_warned2, glob_small_float, glob_optimal_clock_start_sec, glob_not_yet_start_msg, glob_clock_sec, centuries_in_millinium, days_in_year, glob_curr_iter_when_opt, glob_relerr, glob_look_poles, glob_last_good_h, MAX_UNCHANGED, glob_max_trunc_err, glob_abserr, glob_dump_analytic, glob_optimal_start, glob_max_iter, min_in_hour, sec_in_min, #Bottom Generate Globals Decl #BEGIN CONST array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, #END CONST array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x1, array_x2, array_1st_rel_error, array_t, array_last_rel_error, array_pole, array_type_pole, array_x2_init, array_x1_init, array_complex_pole, array_x2_higher, array_real_pole, array_poles, array_x2_higher_work, array_x1_higher_work2, array_x1_higher, array_x2_higher_work2, array_x1_higher_work, glob_last; local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; #TOP DISPLAY ALOT if (iter >= 0) then # if number 1 ind_var := array_t[1]; omniout_float(ALWAYS,"t[1] ",33,ind_var,20," "); analytic_val_y := exact_soln_x1(ind_var); omniout_float(ALWAYS,"x1[1] (analytic) ",33,analytic_val_y,20," "); term_no := 1; numeric_val := array_x1[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS,"x1[1] (numeric) ",33,numeric_val,20," "); if (abs(analytic_val_y) <> 0.0) then # if number 2 relerr := abserr*100.0/abs(analytic_val_y); else relerr := -1.0 ; fi;# end if 2 ; if glob_iter = 1 then # if number 2 array_1st_rel_error[1] := relerr; else array_last_rel_error[1] := relerr; fi;# end if 2 ; omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); omniout_float(ALWAYS,"h ",4,glob_h,20," "); ; analytic_val_y := exact_soln_x2(ind_var); omniout_float(ALWAYS,"x2[1] (analytic) ",33,analytic_val_y,20," "); term_no := 1; numeric_val := array_x2[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS,"x2[1] (numeric) ",33,numeric_val,20," "); if (abs(analytic_val_y) <> 0.0) then # if number 2 relerr := abserr*100.0/abs(analytic_val_y); else relerr := -1.0 ; fi;# end if 2 ; if glob_iter = 1 then # if number 2 array_1st_rel_error[2] := relerr; else array_last_rel_error[2] := relerr; fi;# end if 2 ; omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); omniout_float(ALWAYS,"h ",4,glob_h,20," "); #BOTTOM DISPLAY ALOT fi;# end if 1 ; # End Function number 3 end; # Begin Function number 4 adjust_for_pole := proc(h_param) global DEBUGL, ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_iolevel, #Top Generate Globals Decl glob_iter, glob_current_iter, glob_start, glob_large_float, glob_hmin, hours_in_day, glob_max_opt_iter, glob_html_log, glob_orig_start_sec, glob_smallish_float, glob_no_eqs, glob_max_order, glob_log10_abserr, glob_log10normmin, glob_percent_done, glob_normmax, glob_reached_optimal_h, glob_dump, glob_max_hours, glob_hmin_init, glob_not_yet_finished, glob_almost_1, years_in_century, glob_optimal_expect_sec, glob_log10abserr, glob_warned, glob_log10_relerr, glob_hmax, glob_disp_incr, glob_optimal_done, glob_initial_pass, glob_display_flag, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_h, glob_clock_start_sec, djd_debug2, djd_debug, glob_max_minutes, glob_warned2, glob_small_float, glob_optimal_clock_start_sec, glob_not_yet_start_msg, glob_clock_sec, centuries_in_millinium, days_in_year, glob_curr_iter_when_opt, glob_relerr, glob_look_poles, glob_last_good_h, MAX_UNCHANGED, glob_max_trunc_err, glob_abserr, glob_dump_analytic, glob_optimal_start, glob_max_iter, min_in_hour, sec_in_min, #Bottom Generate Globals Decl #BEGIN CONST array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, #END CONST array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x1, array_x2, array_1st_rel_error, array_t, array_last_rel_error, array_pole, array_type_pole, array_x2_init, array_x1_init, array_complex_pole, array_x2_higher, array_real_pole, array_poles, array_x2_higher_work, array_x1_higher_work2, array_x1_higher, array_x2_higher_work2, array_x1_higher_work, glob_last; local hnew, sz2, tmp; #TOP ADJUST FOR POLE hnew := h_param; glob_normmax := glob_small_float; if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 1 tmp := abs(array_x1_higher[1,1]); if (tmp < glob_normmax) then # if number 2 glob_normmax := tmp; fi;# end if 2 fi;# end if 1 ; if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 1 tmp := abs(array_x2_higher[1,1]); if (tmp < glob_normmax) then # if number 2 glob_normmax := tmp; fi;# end if 2 fi;# end if 1 ; if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 sz2 := array_pole[1]/10.0; if (sz2 < hnew) then # if number 2 omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); omniout_str(INFO,"Reached Optimal"); newline(); return(hnew); fi;# end if 2 fi;# end if 1 ; if (not glob_reached_optimal_h) then # if number 1 glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_t[1]; fi;# end if 1 ; hnew := sz2; #END block #BOTTOM ADJUST FOR POLE # End Function number 4 end; # Begin Function number 5 prog_report := proc(t_start,t_end) global DEBUGL, ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_iolevel, #Top Generate Globals Decl glob_iter, glob_current_iter, glob_start, glob_large_float, glob_hmin, hours_in_day, glob_max_opt_iter, glob_html_log, glob_orig_start_sec, glob_smallish_float, glob_no_eqs, glob_max_order, glob_log10_abserr, glob_log10normmin, glob_percent_done, glob_normmax, glob_reached_optimal_h, glob_dump, glob_max_hours, glob_hmin_init, glob_not_yet_finished, glob_almost_1, years_in_century, glob_optimal_expect_sec, glob_log10abserr, glob_warned, glob_log10_relerr, glob_hmax, glob_disp_incr, glob_optimal_done, glob_initial_pass, glob_display_flag, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_h, glob_clock_start_sec, djd_debug2, djd_debug, glob_max_minutes, glob_warned2, glob_small_float, glob_optimal_clock_start_sec, glob_not_yet_start_msg, glob_clock_sec, centuries_in_millinium, days_in_year, glob_curr_iter_when_opt, glob_relerr, glob_look_poles, glob_last_good_h, MAX_UNCHANGED, glob_max_trunc_err, glob_abserr, glob_dump_analytic, glob_optimal_start, glob_max_iter, min_in_hour, sec_in_min, #Bottom Generate Globals Decl #BEGIN CONST array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, #END CONST array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x1, array_x2, array_1st_rel_error, array_t, array_last_rel_error, array_pole, array_type_pole, array_x2_init, array_x1_init, array_complex_pole, array_x2_higher, array_real_pole, array_poles, array_x2_higher_work, array_x1_higher_work2, array_x1_higher, array_x2_higher_work2, array_x1_higher_work, glob_last; local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; #TOP PROGRESS REPORT clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); percent_done := comp_percent(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO,"Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO,"Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then # if number 1 omniout_str_noeol(INFO,"Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO,"Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); fi;# end if 1 ; omniout_str_noeol(INFO,"Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); #BOTTOM PROGRESS REPORT # End Function number 5 end; # Begin Function number 6 check_for_pole := proc() global DEBUGL, ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_iolevel, #Top Generate Globals Decl glob_iter, glob_current_iter, glob_start, glob_large_float, glob_hmin, hours_in_day, glob_max_opt_iter, glob_html_log, glob_orig_start_sec, glob_smallish_float, glob_no_eqs, glob_max_order, glob_log10_abserr, glob_log10normmin, glob_percent_done, glob_normmax, glob_reached_optimal_h, glob_dump, glob_max_hours, glob_hmin_init, glob_not_yet_finished, glob_almost_1, years_in_century, glob_optimal_expect_sec, glob_log10abserr, glob_warned, glob_log10_relerr, glob_hmax, glob_disp_incr, glob_optimal_done, glob_initial_pass, glob_display_flag, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_h, glob_clock_start_sec, djd_debug2, djd_debug, glob_max_minutes, glob_warned2, glob_small_float, glob_optimal_clock_start_sec, glob_not_yet_start_msg, glob_clock_sec, centuries_in_millinium, days_in_year, glob_curr_iter_when_opt, glob_relerr, glob_look_poles, glob_last_good_h, MAX_UNCHANGED, glob_max_trunc_err, glob_abserr, glob_dump_analytic, glob_optimal_start, glob_max_iter, min_in_hour, sec_in_min, #Bottom Generate Globals Decl #BEGIN CONST array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, #END CONST array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x1, array_x2, array_1st_rel_error, array_t, array_last_rel_error, array_pole, array_type_pole, array_x2_init, array_x1_init, array_complex_pole, array_x2_higher, array_real_pole, array_poles, array_x2_higher_work, array_x1_higher_work2, array_x1_higher, array_x2_higher_work2, array_x1_higher_work, glob_last; local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; #TOP CHECK FOR POLE #IN RADII REAL EQ = 1 #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 #Applies to pole of arbitrary r_order on the real axis, #Due to Prof. George Corliss. n := glob_max_terms; m := n - 1 - 1; while ((m >= 10) and ((abs(array_x1_higher[1,m]) < glob_small_float) or (abs(array_x1_higher[1,m-1]) < glob_small_float) or (abs(array_x1_higher[1,m-2]) < glob_small_float ))) do # do number 2 m := m - 1; od;# end do number 2 ; if (m > 10) then # if number 1 rm0 := array_x1_higher[1,m]/array_x1_higher[1,m-1]; rm1 := array_x1_higher[1,m-1]/array_x1_higher[1,m-2]; hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; if (abs(hdrc) > glob_small_float) then # if number 2 rcs := glob_h/hdrc; ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1,1] := rcs; array_real_pole[1,2] := ord_no; else array_real_pole[1,1] := glob_large_float; array_real_pole[1,2] := glob_large_float; fi;# end if 2 else array_real_pole[1,1] := glob_large_float; array_real_pole[1,2] := glob_large_float; fi;# end if 1 ; #BOTTOM RADII REAL EQ = 1 #IN RADII REAL EQ = 2 #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 #Applies to pole of arbitrary r_order on the real axis, #Due to Prof. George Corliss. n := glob_max_terms; m := n - 2 - 1; while ((m >= 10) and ((abs(array_x2_higher[1,m]) < glob_small_float) or (abs(array_x2_higher[1,m-1]) < glob_small_float) or (abs(array_x2_higher[1,m-2]) < glob_small_float ))) do # do number 2 m := m - 1; od;# end do number 2 ; if (m > 10) then # if number 1 rm0 := array_x2_higher[1,m]/array_x2_higher[1,m-1]; rm1 := array_x2_higher[1,m-1]/array_x2_higher[1,m-2]; hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; if (abs(hdrc) > glob_small_float) then # if number 2 rcs := glob_h/hdrc; ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[2,1] := rcs; array_real_pole[2,2] := ord_no; else array_real_pole[2,1] := glob_large_float; array_real_pole[2,2] := glob_large_float; fi;# end if 2 else array_real_pole[2,1] := glob_large_float; array_real_pole[2,2] := glob_large_float; fi;# end if 1 ; #BOTTOM RADII REAL EQ = 2 #TOP RADII COMPLEX EQ = 1 #Computes radius of convergence for complex conjugate pair of poles. #from 6 adjacent Taylor series terms #Also computes r_order of poles. #Due to Manuel Prieto. #With a correction by Dennis J. Darland n := glob_max_terms - 1 - 1; cnt := 0; while ((cnt < 5) and (n >= 10)) do # do number 2 if (abs(array_x1_higher[1,n]) > glob_small_float) then # if number 1 cnt := cnt + 1; else cnt := 0; fi;# end if 1 ; n := n - 1; od;# end do number 2 ; m := n + cnt; if (m <= 10) then # if number 1 array_complex_pole[1,1] := glob_large_float; array_complex_pole[1,2] := glob_large_float; elif (abs(array_x1_higher[1,m]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-5]) >= (glob_large_float)) then # if number 2 array_complex_pole[1,1] := glob_large_float; array_complex_pole[1,2] := glob_large_float; else rm0 := (array_x1_higher[1,m])/(array_x1_higher[1,m-1]); rm1 := (array_x1_higher[1,m-1])/(array_x1_higher[1,m-2]); rm2 := (array_x1_higher[1,m-2])/(array_x1_higher[1,m-3]); rm3 := (array_x1_higher[1,m-3])/(array_x1_higher[1,m-4]); rm4 := (array_x1_higher[1,m-4])/(array_x1_higher[1,m-5]); nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3 array_complex_pole[1,1] := glob_large_float; array_complex_pole[1,2] := glob_large_float; else if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; if (abs(rcs) > glob_small_float) then # if number 5 if (rcs > 0.0) then # if number 6 rad_c := sqrt(rcs) * glob_h; else rad_c := glob_large_float; fi;# end if 6 else rad_c := glob_large_float; ord_no := glob_large_float; fi;# end if 5 else rad_c := glob_large_float; ord_no := glob_large_float; fi;# end if 4 fi;# end if 3 ; array_complex_pole[1,1] := rad_c; array_complex_pole[1,2] := ord_no; fi;# end if 2 ; #BOTTOM RADII COMPLEX EQ = 1 #TOP RADII COMPLEX EQ = 2 #Computes radius of convergence for complex conjugate pair of poles. #from 6 adjacent Taylor series terms #Also computes r_order of poles. #Due to Manuel Prieto. #With a correction by Dennis J. Darland n := glob_max_terms - 2 - 1; cnt := 0; while ((cnt < 5) and (n >= 10)) do # do number 2 if (abs(array_x2_higher[1,n]) > glob_small_float) then # if number 2 cnt := cnt + 1; else cnt := 0; fi;# end if 2 ; n := n - 1; od;# end do number 2 ; m := n + cnt; if (m <= 10) then # if number 2 array_complex_pole[2,1] := glob_large_float; array_complex_pole[2,2] := glob_large_float; elif (abs(array_x2_higher[1,m]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-5]) >= (glob_large_float)) then # if number 3 array_complex_pole[2,1] := glob_large_float; array_complex_pole[2,2] := glob_large_float; else rm0 := (array_x2_higher[1,m])/(array_x2_higher[1,m-1]); rm1 := (array_x2_higher[1,m-1])/(array_x2_higher[1,m-2]); rm2 := (array_x2_higher[1,m-2])/(array_x2_higher[1,m-3]); rm3 := (array_x2_higher[1,m-3])/(array_x2_higher[1,m-4]); rm4 := (array_x2_higher[1,m-4])/(array_x2_higher[1,m-5]); nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 4 array_complex_pole[2,1] := glob_large_float; array_complex_pole[2,2] := glob_large_float; else if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5 rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; if (abs(rcs) > glob_small_float) then # if number 6 if (rcs > 0.0) then # if number 7 rad_c := sqrt(rcs) * glob_h; else rad_c := glob_large_float; fi;# end if 7 else rad_c := glob_large_float; ord_no := glob_large_float; fi;# end if 6 else rad_c := glob_large_float; ord_no := glob_large_float; fi;# end if 5 fi;# end if 4 ; array_complex_pole[2,1] := rad_c; array_complex_pole[2,2] := ord_no; fi;# end if 3 ; #BOTTOM RADII COMPLEX EQ = 2 found := false; #TOP WHICH RADII EQ = 1 if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3 array_poles[1,1] := array_complex_pole[1,1]; array_poles[1,2] := array_complex_pole[1,2]; found := true; array_type_pole[1] := 2; if (glob_display_flag) then # if number 4 omniout_str(ALWAYS,"Complex estimate of poles used"); fi;# end if 4 ; fi;# end if 3 ; if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 3 array_poles[1,1] := array_real_pole[1,1]; array_poles[1,2] := array_real_pole[1,2]; found := true; array_type_pole[1] := 1; if (glob_display_flag) then # if number 4 omniout_str(ALWAYS,"Real estimate of pole used"); fi;# end if 4 ; fi;# end if 3 ; if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 3 array_poles[1,1] := glob_large_float; array_poles[1,2] := glob_large_float; found := true; array_type_pole[1] := 3; if (glob_display_flag) then # if number 4 omniout_str(ALWAYS,"NO POLE"); fi;# end if 4 ; fi;# end if 3 ; if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 3 array_poles[1,1] := array_real_pole[1,1]; array_poles[1,2] := array_real_pole[1,2]; found := true; array_type_pole[1] := 1; if (glob_display_flag) then # if number 4 omniout_str(ALWAYS,"Real estimate of pole used"); fi;# end if 4 ; fi;# end if 3 ; if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3 array_poles[1,1] := array_complex_pole[1,1]; array_poles[1,2] := array_complex_pole[1,2]; array_type_pole[1] := 2; found := true; if (glob_display_flag) then # if number 4 omniout_str(ALWAYS,"Complex estimate of poles used"); fi;# end if 4 ; fi;# end if 3 ; if not found then # if number 3 array_poles[1,1] := glob_large_float; array_poles[1,2] := glob_large_float; array_type_pole[1] := 3; if (glob_display_flag) then # if number 4 omniout_str(ALWAYS,"NO POLE"); fi;# end if 4 ; fi;# end if 3 ; #BOTTOM WHICH RADII EQ = 1 found := false; #TOP WHICH RADII EQ = 2 if not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3 array_poles[2,1] := array_complex_pole[2,1]; array_poles[2,2] := array_complex_pole[2,2]; found := true; array_type_pole[2] := 2; if (glob_display_flag) then # if number 4 omniout_str(ALWAYS,"Complex estimate of poles used"); fi;# end if 4 ; fi;# end if 3 ; if not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0))) then # if number 3 array_poles[2,1] := array_real_pole[2,1]; array_poles[2,2] := array_real_pole[2,2]; found := true; array_type_pole[2] := 1; if (glob_display_flag) then # if number 4 omniout_str(ALWAYS,"Real estimate of pole used"); fi;# end if 4 ; fi;# end if 3 ; if not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float))) then # if number 3 array_poles[2,1] := glob_large_float; array_poles[2,2] := glob_large_float; found := true; array_type_pole[2] := 3; if (glob_display_flag) then # if number 4 omniout_str(ALWAYS,"NO POLE"); fi;# end if 4 ; fi;# end if 3 ; if not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0)) then # if number 3 array_poles[2,1] := array_real_pole[2,1]; array_poles[2,2] := array_real_pole[2,2]; found := true; array_type_pole[2] := 1; if (glob_display_flag) then # if number 4 omniout_str(ALWAYS,"Real estimate of pole used"); fi;# end if 4 ; fi;# end if 3 ; if not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3 array_poles[2,1] := array_complex_pole[2,1]; array_poles[2,2] := array_complex_pole[2,2]; array_type_pole[2] := 2; found := true; if (glob_display_flag) then # if number 4 omniout_str(ALWAYS,"Complex estimate of poles used"); fi;# end if 4 ; fi;# end if 3 ; if not found then # if number 3 array_poles[2,1] := glob_large_float; array_poles[2,2] := glob_large_float; array_type_pole[2] := 3; if (glob_display_flag) then # if number 4 omniout_str(ALWAYS,"NO POLE"); fi;# end if 4 ; fi;# end if 3 ; #BOTTOM WHICH RADII EQ = 2 array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; #TOP WHICH RADIUS EQ = 1 if array_pole[1] > array_poles[1,1] then # if number 3 array_pole[1] := array_poles[1,1]; array_pole[2] := array_poles[1,2]; fi;# end if 3 ; #BOTTOM WHICH RADIUS EQ = 1 #TOP WHICH RADIUS EQ = 2 if array_pole[1] > array_poles[2,1] then # if number 3 array_pole[1] := array_poles[2,1]; array_pole[2] := array_poles[2,2]; fi;# end if 3 ; #BOTTOM WHICH RADIUS EQ = 2 #BOTTOM CHECK FOR POLE display_pole(); # End Function number 6 end; # Begin Function number 7 get_norms := proc() global DEBUGL, ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_iolevel, #Top Generate Globals Decl glob_iter, glob_current_iter, glob_start, glob_large_float, glob_hmin, hours_in_day, glob_max_opt_iter, glob_html_log, glob_orig_start_sec, glob_smallish_float, glob_no_eqs, glob_max_order, glob_log10_abserr, glob_log10normmin, glob_percent_done, glob_normmax, glob_reached_optimal_h, glob_dump, glob_max_hours, glob_hmin_init, glob_not_yet_finished, glob_almost_1, years_in_century, glob_optimal_expect_sec, glob_log10abserr, glob_warned, glob_log10_relerr, glob_hmax, glob_disp_incr, glob_optimal_done, glob_initial_pass, glob_display_flag, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_h, glob_clock_start_sec, djd_debug2, djd_debug, glob_max_minutes, glob_warned2, glob_small_float, glob_optimal_clock_start_sec, glob_not_yet_start_msg, glob_clock_sec, centuries_in_millinium, days_in_year, glob_curr_iter_when_opt, glob_relerr, glob_look_poles, glob_last_good_h, MAX_UNCHANGED, glob_max_trunc_err, glob_abserr, glob_dump_analytic, glob_optimal_start, glob_max_iter, min_in_hour, sec_in_min, #Bottom Generate Globals Decl #BEGIN CONST array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, #END CONST array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x1, array_x2, array_1st_rel_error, array_t, array_last_rel_error, array_pole, array_type_pole, array_x2_init, array_x1_init, array_complex_pole, array_x2_higher, array_real_pole, array_poles, array_x2_higher_work, array_x1_higher_work2, array_x1_higher, array_x2_higher_work2, array_x1_higher_work, glob_last; local iii; if (not glob_initial_pass) then # if number 3 set_z(array_norms,glob_max_terms+1); #TOP GET NORMS iii := 1; while (iii <= glob_max_terms) do # do number 2 if (abs(array_x1[iii]) > array_norms[iii]) then # if number 4 array_norms[iii] := abs(array_x1[iii]); fi;# end if 4 ; iii := iii + 1; od;# end do number 2 ; iii := 1; while (iii <= glob_max_terms) do # do number 2 if (abs(array_x2[iii]) > array_norms[iii]) then # if number 4 array_norms[iii] := abs(array_x2[iii]); fi;# end if 4 ; iii := iii + 1; od;# end do number 2 #GET NORMS ; fi;# end if 3 ; # End Function number 7 end; # Begin Function number 8 atomall := proc() global DEBUGL, ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_iolevel, #Top Generate Globals Decl glob_iter, glob_current_iter, glob_start, glob_large_float, glob_hmin, hours_in_day, glob_max_opt_iter, glob_html_log, glob_orig_start_sec, glob_smallish_float, glob_no_eqs, glob_max_order, glob_log10_abserr, glob_log10normmin, glob_percent_done, glob_normmax, glob_reached_optimal_h, glob_dump, glob_max_hours, glob_hmin_init, glob_not_yet_finished, glob_almost_1, years_in_century, glob_optimal_expect_sec, glob_log10abserr, glob_warned, glob_log10_relerr, glob_hmax, glob_disp_incr, glob_optimal_done, glob_initial_pass, glob_display_flag, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_h, glob_clock_start_sec, djd_debug2, djd_debug, glob_max_minutes, glob_warned2, glob_small_float, glob_optimal_clock_start_sec, glob_not_yet_start_msg, glob_clock_sec, centuries_in_millinium, days_in_year, glob_curr_iter_when_opt, glob_relerr, glob_look_poles, glob_last_good_h, MAX_UNCHANGED, glob_max_trunc_err, glob_abserr, glob_dump_analytic, glob_optimal_start, glob_max_iter, min_in_hour, sec_in_min, #Bottom Generate Globals Decl #BEGIN CONST array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, #END CONST array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x1, array_x2, array_1st_rel_error, array_t, array_last_rel_error, array_pole, array_type_pole, array_x2_init, array_x1_init, array_complex_pole, array_x2_higher, array_real_pole, array_poles, array_x2_higher_work, array_x1_higher_work2, array_x1_higher, array_x2_higher_work2, array_x1_higher_work, glob_last; local kkk, order_d, adj2, temporary, term; #TOP ATOMALL #END OUTFILE1 #BEGIN ATOMHDR1 # emit pre mult $eq_no = 1 i = 1 array_tmp1[1] := (array_const_4D0[1] * (array_x2[1])); #emit pre add $eq_no = 1 i = 1 array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; #emit pre diff $eq_no = 1 i = 1 array_tmp3[1] := array_x2_higher[2,1]; # emit pre mult $eq_no = 1 i = 1 array_tmp4[1] := (array_const_2D0[1] * (array_tmp3[1])); #emit pre sub $eq_no = 1 i = 1 array_tmp5[1] := (array_tmp2[1] - (array_tmp4[1])); # emit pre mult $eq_no = 1 i = 1 array_tmp6[1] := (array_const_2D0[1] * (array_x1[1])); #emit pre sub $eq_no = 1 i = 1 array_tmp7[1] := (array_tmp5[1] - (array_tmp6[1])); #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 if (1 <= glob_max_terms) then # if number 1 temporary := array_tmp7[1] * (glob_h ^ (1)) * factorial_3(0,1); array_x1[2] := temporary; array_x1_higher[1,2] := temporary; temporary := temporary / glob_h * (2.0); array_x1_higher[2,1] := temporary ; fi;# end if 1 ; kkk := 2; #emit pre diff $eq_no = 2 i = 1 array_tmp9[1] := array_x2_higher[2,1]; # emit pre mult $eq_no = 2 i = 1 array_tmp10[1] := (array_const_3D0[1] * (array_tmp9[1])); # emit pre mult $eq_no = 2 i = 1 array_tmp11[1] := (array_const_2D0[1] * (array_x2[1])); #emit pre sub $eq_no = 2 i = 1 array_tmp12[1] := (array_tmp10[1] - (array_tmp11[1])); #emit pre diff $eq_no = 2 i = 1 array_tmp13[1] := array_x1_higher[3,1]; #emit pre sub $eq_no = 2 i = 1 array_tmp14[1] := (array_tmp12[1] - (array_tmp13[1])); #emit pre diff $eq_no = 2 i = 1 array_tmp15[1] := array_x1_higher[2,1]; #emit pre sub $eq_no = 2 i = 1 array_tmp16[1] := (array_tmp14[1] - (array_tmp15[1])); #emit pre add $eq_no = 2 i = 1 array_tmp17[1] := array_tmp16[1] + array_x1[1]; #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 if (1 <= glob_max_terms) then # if number 1 temporary := array_tmp17[1] * (glob_h ^ (2)) * factorial_3(0,2); array_x2[3] := temporary; array_x2_higher[1,3] := temporary; temporary := temporary / glob_h * (2.0); array_x2_higher[2,2] := temporary ; temporary := temporary / glob_h * (3.0); array_x2_higher[3,1] := temporary ; fi;# end if 1 ; kkk := 2; #END ATOMHDR1 #BEGIN ATOMHDR2 # emit pre mult $eq_no = 1 i = 2 array_tmp1[2] := ats(2,array_const_4D0,array_x2,1); #emit pre add $eq_no = 1 i = 2 array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; #emit pre diff $eq_no = 1 i = 2 array_tmp3[2] := array_x2_higher[2,2]; # emit pre mult $eq_no = 1 i = 2 array_tmp4[2] := ats(2,array_const_2D0,array_tmp3,1); #emit pre sub $eq_no = 1 i = 2 array_tmp5[2] := (array_tmp2[2] - (array_tmp4[2])); # emit pre mult $eq_no = 1 i = 2 array_tmp6[2] := ats(2,array_const_2D0,array_x1,1); #emit pre sub $eq_no = 1 i = 2 array_tmp7[2] := (array_tmp5[2] - (array_tmp6[2])); #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 if (2 <= glob_max_terms) then # if number 1 temporary := array_tmp7[2] * (glob_h ^ (1)) * factorial_3(1,2); array_x1[3] := temporary; array_x1_higher[1,3] := temporary; temporary := temporary / glob_h * (2.0); array_x1_higher[2,2] := temporary ; fi;# end if 1 ; kkk := 3; #emit pre diff $eq_no = 2 i = 2 array_tmp9[2] := array_x2_higher[2,2]; # emit pre mult $eq_no = 2 i = 2 array_tmp10[2] := ats(2,array_const_3D0,array_tmp9,1); # emit pre mult $eq_no = 2 i = 2 array_tmp11[2] := ats(2,array_const_2D0,array_x2,1); #emit pre sub $eq_no = 2 i = 2 array_tmp12[2] := (array_tmp10[2] - (array_tmp11[2])); #emit pre diff $eq_no = 2 i = 2 array_tmp13[2] := array_x1_higher[3,2]; #emit pre sub $eq_no = 2 i = 2 array_tmp14[2] := (array_tmp12[2] - (array_tmp13[2])); #emit pre diff $eq_no = 2 i = 2 array_tmp15[2] := array_x1_higher[2,2]; #emit pre sub $eq_no = 2 i = 2 array_tmp16[2] := (array_tmp14[2] - (array_tmp15[2])); #emit pre add $eq_no = 2 i = 2 array_tmp17[2] := array_tmp16[2] + array_x1[2]; #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 if (2 <= glob_max_terms) then # if number 1 temporary := array_tmp17[2] * (glob_h ^ (2)) * factorial_3(1,3); array_x2[4] := temporary; array_x2_higher[1,4] := temporary; temporary := temporary / glob_h * (2.0); array_x2_higher[2,3] := temporary ; temporary := temporary / glob_h * (3.0); array_x2_higher[3,2] := temporary ; fi;# end if 1 ; kkk := 3; #END ATOMHDR2 #BEGIN ATOMHDR3 # emit pre mult $eq_no = 1 i = 3 array_tmp1[3] := ats(3,array_const_4D0,array_x2,1); #emit pre add $eq_no = 1 i = 3 array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; #emit pre diff $eq_no = 1 i = 3 array_tmp3[3] := array_x2_higher[2,3]; # emit pre mult $eq_no = 1 i = 3 array_tmp4[3] := ats(3,array_const_2D0,array_tmp3,1); #emit pre sub $eq_no = 1 i = 3 array_tmp5[3] := (array_tmp2[3] - (array_tmp4[3])); # emit pre mult $eq_no = 1 i = 3 array_tmp6[3] := ats(3,array_const_2D0,array_x1,1); #emit pre sub $eq_no = 1 i = 3 array_tmp7[3] := (array_tmp5[3] - (array_tmp6[3])); #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 if (3 <= glob_max_terms) then # if number 1 temporary := array_tmp7[3] * (glob_h ^ (1)) * factorial_3(2,3); array_x1[4] := temporary; array_x1_higher[1,4] := temporary; temporary := temporary / glob_h * (2.0); array_x1_higher[2,3] := temporary ; fi;# end if 1 ; kkk := 4; #emit pre diff $eq_no = 2 i = 3 array_tmp9[3] := array_x2_higher[2,3]; # emit pre mult $eq_no = 2 i = 3 array_tmp10[3] := ats(3,array_const_3D0,array_tmp9,1); # emit pre mult $eq_no = 2 i = 3 array_tmp11[3] := ats(3,array_const_2D0,array_x2,1); #emit pre sub $eq_no = 2 i = 3 array_tmp12[3] := (array_tmp10[3] - (array_tmp11[3])); #emit pre diff $eq_no = 2 i = 3 array_tmp13[3] := array_x1_higher[3,3]; #emit pre sub $eq_no = 2 i = 3 array_tmp14[3] := (array_tmp12[3] - (array_tmp13[3])); #emit pre diff $eq_no = 2 i = 3 array_tmp15[3] := array_x1_higher[2,3]; #emit pre sub $eq_no = 2 i = 3 array_tmp16[3] := (array_tmp14[3] - (array_tmp15[3])); #emit pre add $eq_no = 2 i = 3 array_tmp17[3] := array_tmp16[3] + array_x1[3]; #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 if (3 <= glob_max_terms) then # if number 1 temporary := array_tmp17[3] * (glob_h ^ (2)) * factorial_3(2,4); array_x2[5] := temporary; array_x2_higher[1,5] := temporary; temporary := temporary / glob_h * (2.0); array_x2_higher[2,4] := temporary ; temporary := temporary / glob_h * (3.0); array_x2_higher[3,3] := temporary ; fi;# end if 1 ; kkk := 4; #END ATOMHDR3 #BEGIN ATOMHDR4 # emit pre mult $eq_no = 1 i = 4 array_tmp1[4] := ats(4,array_const_4D0,array_x2,1); #emit pre add $eq_no = 1 i = 4 array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; #emit pre diff $eq_no = 1 i = 4 array_tmp3[4] := array_x2_higher[2,4]; # emit pre mult $eq_no = 1 i = 4 array_tmp4[4] := ats(4,array_const_2D0,array_tmp3,1); #emit pre sub $eq_no = 1 i = 4 array_tmp5[4] := (array_tmp2[4] - (array_tmp4[4])); # emit pre mult $eq_no = 1 i = 4 array_tmp6[4] := ats(4,array_const_2D0,array_x1,1); #emit pre sub $eq_no = 1 i = 4 array_tmp7[4] := (array_tmp5[4] - (array_tmp6[4])); #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 if (4 <= glob_max_terms) then # if number 1 temporary := array_tmp7[4] * (glob_h ^ (1)) * factorial_3(3,4); array_x1[5] := temporary; array_x1_higher[1,5] := temporary; temporary := temporary / glob_h * (2.0); array_x1_higher[2,4] := temporary ; fi;# end if 1 ; kkk := 5; #emit pre diff $eq_no = 2 i = 4 array_tmp9[4] := array_x2_higher[2,4]; # emit pre mult $eq_no = 2 i = 4 array_tmp10[4] := ats(4,array_const_3D0,array_tmp9,1); # emit pre mult $eq_no = 2 i = 4 array_tmp11[4] := ats(4,array_const_2D0,array_x2,1); #emit pre sub $eq_no = 2 i = 4 array_tmp12[4] := (array_tmp10[4] - (array_tmp11[4])); #emit pre diff $eq_no = 2 i = 4 array_tmp13[4] := array_x1_higher[3,4]; #emit pre sub $eq_no = 2 i = 4 array_tmp14[4] := (array_tmp12[4] - (array_tmp13[4])); #emit pre diff $eq_no = 2 i = 4 array_tmp15[4] := array_x1_higher[2,4]; #emit pre sub $eq_no = 2 i = 4 array_tmp16[4] := (array_tmp14[4] - (array_tmp15[4])); #emit pre add $eq_no = 2 i = 4 array_tmp17[4] := array_tmp16[4] + array_x1[4]; #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 if (4 <= glob_max_terms) then # if number 1 temporary := array_tmp17[4] * (glob_h ^ (2)) * factorial_3(3,5); array_x2[6] := temporary; array_x2_higher[1,6] := temporary; temporary := temporary / glob_h * (2.0); array_x2_higher[2,5] := temporary ; temporary := temporary / glob_h * (3.0); array_x2_higher[3,4] := temporary ; fi;# end if 1 ; kkk := 5; #END ATOMHDR4 #BEGIN ATOMHDR5 # emit pre mult $eq_no = 1 i = 5 array_tmp1[5] := ats(5,array_const_4D0,array_x2,1); #emit pre add $eq_no = 1 i = 5 array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; #emit pre diff $eq_no = 1 i = 5 array_tmp3[5] := array_x2_higher[2,5]; # emit pre mult $eq_no = 1 i = 5 array_tmp4[5] := ats(5,array_const_2D0,array_tmp3,1); #emit pre sub $eq_no = 1 i = 5 array_tmp5[5] := (array_tmp2[5] - (array_tmp4[5])); # emit pre mult $eq_no = 1 i = 5 array_tmp6[5] := ats(5,array_const_2D0,array_x1,1); #emit pre sub $eq_no = 1 i = 5 array_tmp7[5] := (array_tmp5[5] - (array_tmp6[5])); #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 if (5 <= glob_max_terms) then # if number 1 temporary := array_tmp7[5] * (glob_h ^ (1)) * factorial_3(4,5); array_x1[6] := temporary; array_x1_higher[1,6] := temporary; temporary := temporary / glob_h * (2.0); array_x1_higher[2,5] := temporary ; fi;# end if 1 ; kkk := 6; #emit pre diff $eq_no = 2 i = 5 array_tmp9[5] := array_x2_higher[2,5]; # emit pre mult $eq_no = 2 i = 5 array_tmp10[5] := ats(5,array_const_3D0,array_tmp9,1); # emit pre mult $eq_no = 2 i = 5 array_tmp11[5] := ats(5,array_const_2D0,array_x2,1); #emit pre sub $eq_no = 2 i = 5 array_tmp12[5] := (array_tmp10[5] - (array_tmp11[5])); #emit pre diff $eq_no = 2 i = 5 array_tmp13[5] := array_x1_higher[3,5]; #emit pre sub $eq_no = 2 i = 5 array_tmp14[5] := (array_tmp12[5] - (array_tmp13[5])); #emit pre diff $eq_no = 2 i = 5 array_tmp15[5] := array_x1_higher[2,5]; #emit pre sub $eq_no = 2 i = 5 array_tmp16[5] := (array_tmp14[5] - (array_tmp15[5])); #emit pre add $eq_no = 2 i = 5 array_tmp17[5] := array_tmp16[5] + array_x1[5]; #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 if (5 <= glob_max_terms) then # if number 1 temporary := array_tmp17[5] * (glob_h ^ (2)) * factorial_3(4,6); array_x2[7] := temporary; array_x2_higher[1,7] := temporary; temporary := temporary / glob_h * (2.0); array_x2_higher[2,6] := temporary ; temporary := temporary / glob_h * (3.0); array_x2_higher[3,5] := temporary ; fi;# end if 1 ; kkk := 6; #END ATOMHDR5 #BEGIN OUTFILE3 #Top Atomall While Loop-- outfile3 while (kkk <= glob_max_terms) do # do number 1 #END OUTFILE3 #BEGIN OUTFILE4 #emit mult $eq_no = 1 array_tmp1[kkk] := ats(kkk,array_const_4D0,array_x2,1); #emit add $eq_no = 1 array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; #emit diff $eq_no = 1 array_tmp3[kkk] := array_x2_higher[2,kkk]; #emit mult $eq_no = 1 array_tmp4[kkk] := ats(kkk,array_const_2D0,array_tmp3,1); #emit sub $eq_no = 1 array_tmp5[kkk] := (array_tmp2[kkk] - (array_tmp4[kkk])); #emit mult $eq_no = 1 array_tmp6[kkk] := ats(kkk,array_const_2D0,array_x1,1); #emit sub $eq_no = 1 array_tmp7[kkk] := (array_tmp5[kkk] - (array_tmp6[kkk])); #emit assign $eq_no = 1 order_d := 1; if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 temporary := array_tmp7[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); array_x1[kkk + order_d] := temporary; array_x1_higher[1,kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 temporary := temporary / glob_h * convfp(adj2); array_x1_higher[adj2,term] := temporary; adj2 := adj2 + 1; term := term - 1; od;# end do number 2 fi;# end if 1 ; #emit diff $eq_no = 2 array_tmp9[kkk] := array_x2_higher[2,kkk]; #emit mult $eq_no = 2 array_tmp10[kkk] := ats(kkk,array_const_3D0,array_tmp9,1); #emit mult $eq_no = 2 array_tmp11[kkk] := ats(kkk,array_const_2D0,array_x2,1); #emit sub $eq_no = 2 array_tmp12[kkk] := (array_tmp10[kkk] - (array_tmp11[kkk])); #emit diff $eq_no = 2 array_tmp13[kkk] := array_x1_higher[3,kkk]; #emit sub $eq_no = 2 array_tmp14[kkk] := (array_tmp12[kkk] - (array_tmp13[kkk])); #emit diff $eq_no = 2 array_tmp15[kkk] := array_x1_higher[2,kkk]; #emit sub $eq_no = 2 array_tmp16[kkk] := (array_tmp14[kkk] - (array_tmp15[kkk])); #emit add $eq_no = 2 array_tmp17[kkk] := array_tmp16[kkk] + array_x1[kkk]; #emit assign $eq_no = 2 order_d := 2; if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 temporary := array_tmp17[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); array_x2[kkk + order_d] := temporary; array_x2_higher[1,kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 temporary := temporary / glob_h * convfp(adj2); array_x2_higher[adj2,term] := temporary; adj2 := adj2 + 1; term := term - 1; od;# end do number 2 fi;# end if 1 ; kkk := kkk + 1; od;# end do number 1 ; #BOTTOM ATOMALL #END OUTFILE4 #BEGIN OUTFILE5 # End Function number 8 end; #BEGIN ATS LIBRARY BLOCK omniout_str := proc(iolevel,str) global glob_iolevel; if (glob_iolevel >= iolevel) then printf("%s\n",str); fi; # End Function number 1 end; omniout_str_noeol := proc(iolevel,str) global glob_iolevel; if (glob_iolevel >= iolevel) then printf("%s",str); fi; # End Function number 1 end; omniout_labstr := proc(iolevel,label,str) global glob_iolevel; if (glob_iolevel >= iolevel) then print(label,str); fi; # End Function number 1 end; omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) global glob_iolevel; if (glob_iolevel >= iolevel) then if vallen = 4 then printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); else printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); fi; fi; # End Function number 1 end; omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) global glob_iolevel; if (glob_iolevel >= iolevel) then if vallen = 5 then printf("%-30s = %-32d %s\n",prelabel,value, postlabel); else printf("%-30s = %-32d %s \n",prelabel,value, postlabel); fi; fi; # End Function number 1 end; omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) global glob_iolevel; if (glob_iolevel >= iolevel) then print(prelabel,"[",elemnt,"]",value, postlabel); fi; # End Function number 1 end; dump_series := proc(iolevel,dump_label,series_name, array_series,numb) global glob_iolevel; local i; if (glob_iolevel >= iolevel) then i := 1; while (i <= numb) do print(dump_label,series_name ,i,array_series[i]); i := i + 1; od; fi; # End Function number 1 end; dump_series_2 := proc(iolevel,dump_label,series_name2, array_series2,numb,subnum,array_x) global glob_iolevel; local i,sub,ts_term; if (glob_iolevel >= iolevel) then sub := 1; while (sub <= subnum) do i := 1; while (i <= numb) do print(dump_label,series_name2,sub,i,array_series2[sub,i]); od; sub := sub + 1; od; fi; # End Function number 1 end; cs_info := proc(iolevel,str) global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; if (glob_iolevel >= iolevel) then print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) fi; # End Function number 1 end; # Begin Function number 2 logitem_time := proc(fd,secs_in) global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; secs := (secs_in); if (secs > 0.0) then # if number 1 sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); milliniums := convfloat(secs / sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int) * years_in_century; years_int := floor(years); days := (years - years_int) * days_in_year; days_int := floor(days); hours := (days - days_int) * hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int) * min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int) * sec_in_min; sec_int := floor(seconds); fprintf(fd,""); if (millinium_int > 0) then # if number 2 fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); elif (cent_int > 0) then # if number 3 fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); elif (years_int > 0) then # if number 4 fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); elif (days_int > 0) then # if number 5 fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); elif (hours_int > 0) then # if number 6 fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); elif (minutes_int > 0) then # if number 7 fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); else fprintf(fd,"%d Seconds",sec_int); fi;# end if 7 else fprintf(fd,"Unknown"); fi;# end if 6 fprintf(fd,""); # End Function number 2 end; omniout_timestr := proc (secs_in) global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; secs := convfloat(secs_in); if (secs > 0.0) then # if number 6 sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); milliniums := convfloat(secs / sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int) * years_in_century; years_int := floor(years); days := (years - years_int) * days_in_year; days_int := floor(days); hours := (days - days_int) * hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int) * min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int) * sec_in_min; sec_int := floor(seconds); if (millinium_int > 0) then # if number 7 printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); elif (cent_int > 0) then # if number 8 printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); elif (years_int > 0) then # if number 9 printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); elif (days_int > 0) then # if number 10 printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); elif (hours_int > 0) then # if number 11 printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); elif (minutes_int > 0) then # if number 12 printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); else printf(" = %d Seconds\n",sec_int); fi;# end if 12 else printf(" Unknown\n"); fi;# end if 11 # End Function number 2 end; # Begin Function number 3 ats := proc( mmm_ats,array_a,array_b,jjj_ats) local iii_ats, lll_ats,ma_ats, ret_ats; ret_ats := 0.0; if (jjj_ats <= mmm_ats) then # if number 11 ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while (iii_ats <= mmm_ats) do # do number 1 lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1; od;# end do number 1 fi;# end if 11 ; ret_ats # End Function number 3 end; # Begin Function number 4 att := proc( mmm_att,array_aa,array_bb,jjj_att) global glob_max_terms; local al_att, iii_att,lll_att, ma_att, ret_att; ret_att := 0.0; if (jjj_att <= mmm_att) then # if number 11 ma_att := mmm_att + 2; iii_att := jjj_att; while (iii_att <= mmm_att) do # do number 1 lll_att := ma_att - iii_att; al_att := (lll_att - 1); if (lll_att <= glob_max_terms) then # if number 12 ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); fi;# end if 12 ; iii_att := iii_att + 1; od;# end do number 1 ; ret_att := ret_att / convfp(mmm_att) ; fi;# end if 11 ; ret_att; # End Function number 4 end; # Begin Function number 5 display_pole := proc() global ALWAYS,glob_display_flag, glob_large_float, array_pole; if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); fi;# end if 11 # End Function number 5 end; # Begin Function number 6 logditto := proc(file) fprintf(file,""); fprintf(file,"ditto"); fprintf(file,""); # End Function number 6 end; # Begin Function number 7 logitem_integer := proc(file,n) fprintf(file,""); fprintf(file,"%d",n); fprintf(file,""); # End Function number 7 end; # Begin Function number 8 logitem_str := proc(file,str) fprintf(file,""); fprintf(file,str); fprintf(file,""); # End Function number 8 end; # Begin Function number 9 log_revs := proc(file,revs) fprintf(file,revs); # End Function number 9 end; # Begin Function number 10 logitem_float := proc(file,x) fprintf(file,""); fprintf(file,"%g",x); fprintf(file,""); # End Function number 10 end; # Begin Function number 11 logitem_pole := proc(file,pole) fprintf(file,""); if pole = 0 then # if number 11 fprintf(file,"NA"); elif pole = 1 then # if number 12 fprintf(file,"Real"); elif pole = 2 then # if number 13 fprintf(file,"Complex"); else fprintf(file,"No Pole"); fi;# end if 13 fprintf(file,""); # End Function number 11 end; # Begin Function number 12 logstart := proc(file) fprintf(file,""); # End Function number 12 end; # Begin Function number 13 logend := proc(file) fprintf(file,"\n"); # End Function number 13 end; # Begin Function number 14 chk_data := proc() global glob_max_iter,ALWAYS, glob_max_terms; local errflag; errflag := false; if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); glob_max_terms := 30; fi;# end if 13 ; if (glob_max_iter < 2) then # if number 13 omniout_str(ALWAYS,"Illegal max_iter"); errflag := true; fi;# end if 13 ; if (errflag) then # if number 13 quit; fi;# end if 13 # End Function number 14 end; # Begin Function number 15 comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) global glob_small_float; local ms2, rrr, sec_left, sub1, sub2; ; ms2 := clock_sec; sub1 := (t_end2-t_start2); sub2 := (t2-t_start2); if (sub1 = 0.0) then # if number 13 sec_left := 0.0; else if (abs(sub2) > 0.0) then # if number 14 rrr := (sub1/sub2); sec_left := rrr * ms2 - ms2; else sec_left := 0.0; fi;# end if 14 fi;# end if 13 ; sec_left; # End Function number 15 end; # Begin Function number 16 comp_percent := proc(t_end2,t_start2,t2) global glob_small_float; local rrr, sub1, sub2; sub1 := (t_end2-t_start2); sub2 := (t2-t_start2); if (abs(sub2) > glob_small_float) then # if number 13 rrr := (100.0*sub2)/sub1; else rrr := 0.0; fi;# end if 13 ; rrr # End Function number 16 end; # Begin Function number 17 factorial_1 := proc(nnn) nnn!; # End Function number 17 end; # Begin Function number 18 factorial_3 := proc(mmm2,nnn2) (mmm2!)/(nnn2!); # End Function number 18 end; # Begin Function number 19 convfp := proc(mmm) (mmm); # End Function number 19 end; # Begin Function number 20 convfloat := proc(mmm) (mmm); # End Function number 20 end; elapsed_time_seconds := proc() time(); end; #END ATS LIBRARY BLOCK #BEGIN USER DEF BLOCK #BEGIN USER DEF BLOCK exact_soln_x1 := proc(t) local c1,c2,c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0 * c1 + 6.0 * c3 * exp(-t); end; exact_soln_x2 := proc(t) local c1,c2,c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; c1 + c2 * exp(2.0 * t) + c3 * exp(-t); end; exact_soln_x2p := proc(t) local c1,c2,c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t); end; #END USER DEF BLOCK #END USER DEF BLOCK #END OUTFILE5 # Begin Function number 2 mainprog := proc() #BEGIN OUTFIEMAIN local d1,d2,d3,d4,est_err_2,niii,done_once, term,ord,order_diff,term_no,html_log_file, rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, t_start,t_end ,it, log10norm, max_terms, opt_iter, tmp; #Top Generate Globals Definition #Bottom Generate Globals Deninition global DEBUGL, ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_iolevel, #Top Generate Globals Decl glob_iter, glob_current_iter, glob_start, glob_large_float, glob_hmin, hours_in_day, glob_max_opt_iter, glob_html_log, glob_orig_start_sec, glob_smallish_float, glob_no_eqs, glob_max_order, glob_log10_abserr, glob_log10normmin, glob_percent_done, glob_normmax, glob_reached_optimal_h, glob_dump, glob_max_hours, glob_hmin_init, glob_not_yet_finished, glob_almost_1, years_in_century, glob_optimal_expect_sec, glob_log10abserr, glob_warned, glob_log10_relerr, glob_hmax, glob_disp_incr, glob_optimal_done, glob_initial_pass, glob_display_flag, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_h, glob_clock_start_sec, djd_debug2, djd_debug, glob_max_minutes, glob_warned2, glob_small_float, glob_optimal_clock_start_sec, glob_not_yet_start_msg, glob_clock_sec, centuries_in_millinium, days_in_year, glob_curr_iter_when_opt, glob_relerr, glob_look_poles, glob_last_good_h, MAX_UNCHANGED, glob_max_trunc_err, glob_abserr, glob_dump_analytic, glob_optimal_start, glob_max_iter, min_in_hour, sec_in_min, #Bottom Generate Globals Decl #BEGIN CONST array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, #END CONST array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x1, array_x2, array_1st_rel_error, array_t, array_last_rel_error, array_pole, array_type_pole, array_x2_init, array_x1_init, array_complex_pole, array_x2_higher, array_real_pole, array_poles, array_x2_higher_work, array_x1_higher_work2, array_x1_higher, array_x2_higher_work2, array_x1_higher_work, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGL := 3; ALWAYS := 1; DEBUGMASSIVE := 4; glob_max_terms := 30; INFO := 2; glob_iolevel := 5; glob_iter := 0; glob_current_iter := 0; glob_start := 0; glob_large_float := 9.0e100; glob_hmin := 0.00000000001; hours_in_day := 24.0; glob_max_opt_iter := 10; glob_html_log := true; glob_orig_start_sec := 0.0; glob_smallish_float := 0.1e-100; glob_no_eqs := 0; glob_max_order := 30; glob_log10_abserr := 0.1e-10; glob_log10normmin := 0.1; glob_percent_done := 0.0; glob_normmax := 0.0; glob_reached_optimal_h := false; glob_dump := false; glob_max_hours := 0.0; glob_hmin_init := 0.001; glob_not_yet_finished := true; glob_almost_1 := 0.9990; years_in_century := 100.0; glob_optimal_expect_sec := 0.1; glob_log10abserr := 0.0; glob_warned := false; glob_log10_relerr := 0.1e-10; glob_hmax := 1.0; glob_disp_incr := 0.1; glob_optimal_done := false; glob_initial_pass := true; glob_display_flag := true; glob_log10relerr := 0.0; glob_max_sec := 10000.0; glob_unchanged_h_cnt := 0; glob_max_rel_trunc_err := 0.1e-10; glob_h := 0.1; glob_clock_start_sec := 0.0; djd_debug2 := true; djd_debug := true; glob_max_minutes := 0.0; glob_warned2 := false; glob_small_float := 0.1e-50; glob_optimal_clock_start_sec := 0.0; glob_not_yet_start_msg := true; glob_clock_sec := 0.0; centuries_in_millinium := 10.0; days_in_year := 365.0; glob_curr_iter_when_opt := 0; glob_relerr := 0.1e-10; glob_look_poles := false; glob_last_good_h := 0.1; MAX_UNCHANGED := 10; glob_max_trunc_err := 0.1e-10; glob_abserr := 0.1e-10; glob_dump_analytic := false; glob_optimal_start := 0.0; glob_max_iter := 1000; min_in_hour := 60.0; sec_in_min := 60.0; #Write Set Defaults glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_max_order := 2; glob_no_eqs := 2; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.0; glob_max_minutes := 15.0; omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS,"##############temp/complicated2postode.ode#################"); omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); omniout_str(ALWAYS,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"); omniout_str(ALWAYS,"!"); omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS,"Digits := 32;"); omniout_str(ALWAYS,"max_terms := 30;"); omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); omniout_str(ALWAYS,"!"); omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS,"t_start := 0.5;"); omniout_str(ALWAYS,"t_end := 5.0;"); omniout_str(ALWAYS,"array_x1_init[1] := exact_soln_x1(t_start);"); omniout_str(ALWAYS,"array_x2_init[1] := exact_soln_x2(t_start);"); omniout_str(ALWAYS,"array_x2_init[2] := exact_soln_x2p(t_start);"); omniout_str(ALWAYS,"glob_h := 0.00001 ;"); omniout_str(ALWAYS,"glob_look_poles := true;"); omniout_str(ALWAYS,"glob_max_iter := 10;"); omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS,"glob_h := 0.00005 ;"); omniout_str(ALWAYS,"glob_look_poles := true;"); omniout_str(ALWAYS,"glob_max_iter := 100;"); omniout_str(ALWAYS,"glob_max_minutes := 15;"); omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); omniout_str(ALWAYS,"!"); omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS,"exact_soln_x1 := proc(t)"); omniout_str(ALWAYS,"local c1,c2,c3;"); omniout_str(ALWAYS,"c1 := 0.0001;"); omniout_str(ALWAYS,"c2 := 0.0002;"); omniout_str(ALWAYS,"c3 := 0.0003;"); omniout_str(ALWAYS,"2.0 * c1 + 6.0 * c3 * exp(-t);"); omniout_str(ALWAYS,"end;"); omniout_str(ALWAYS,"exact_soln_x2 := proc(t)"); omniout_str(ALWAYS,"local c1,c2,c3;"); omniout_str(ALWAYS,"c1 := 0.0001;"); omniout_str(ALWAYS,"c2 := 0.0002;"); omniout_str(ALWAYS,"c3 := 0.0003;"); omniout_str(ALWAYS,"c1 + c2 * exp(2.0 * t) + c3 * exp(-t);"); omniout_str(ALWAYS,"end;"); omniout_str(ALWAYS,"exact_soln_x2p := proc(t)"); omniout_str(ALWAYS,"local c1,c2,c3;"); omniout_str(ALWAYS,"c1 := 0.0001;"); omniout_str(ALWAYS,"c2 := 0.0002;"); omniout_str(ALWAYS,"c3 := 0.0003;"); omniout_str(ALWAYS,"2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);"); omniout_str(ALWAYS,"end;"); omniout_str(ALWAYS,"#END USER DEF BLOCK"); omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 1.0e-200; glob_smallish_float := 1.0e-64; glob_large_float := 1.0e100; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; #BEGIN FIRST INPUT BLOCK #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; #END FIRST INPUT BLOCK #END FIRST INPUT BLOCK #START OF INITS AFTER INPUT BLOCK glob_max_terms := max_terms; glob_html_log := true; #END OF INITS AFTER INPUT BLOCK array_norms:= Array(1..(max_terms + 1),[]); array_tmp0:= Array(1..(max_terms + 1),[]); array_tmp1:= Array(1..(max_terms + 1),[]); array_tmp2:= Array(1..(max_terms + 1),[]); array_tmp3:= Array(1..(max_terms + 1),[]); array_tmp4:= Array(1..(max_terms + 1),[]); array_tmp5:= Array(1..(max_terms + 1),[]); array_tmp6:= Array(1..(max_terms + 1),[]); array_tmp7:= Array(1..(max_terms + 1),[]); array_tmp8:= Array(1..(max_terms + 1),[]); array_tmp9:= Array(1..(max_terms + 1),[]); array_tmp10:= Array(1..(max_terms + 1),[]); array_tmp11:= Array(1..(max_terms + 1),[]); array_tmp12:= Array(1..(max_terms + 1),[]); array_tmp13:= Array(1..(max_terms + 1),[]); array_tmp14:= Array(1..(max_terms + 1),[]); array_tmp15:= Array(1..(max_terms + 1),[]); array_tmp16:= Array(1..(max_terms + 1),[]); array_tmp17:= Array(1..(max_terms + 1),[]); array_m1:= Array(1..(max_terms + 1),[]); array_x1:= Array(1..(max_terms + 1),[]); array_x2:= Array(1..(max_terms + 1),[]); array_1st_rel_error:= Array(1..(max_terms + 1),[]); array_t:= Array(1..(max_terms + 1),[]); array_last_rel_error:= Array(1..(max_terms + 1),[]); array_pole:= Array(1..(max_terms + 1),[]); array_type_pole:= Array(1..(max_terms + 1),[]); array_x2_init:= Array(1..(max_terms + 1),[]); array_x1_init:= Array(1..(max_terms + 1),[]); array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]); array_x2_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); array_x1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); array_x1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); term := 1; while term <= max_terms do # do number 2 array_norms[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_tmp0[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_tmp1[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_tmp2[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_tmp3[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_tmp4[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_tmp5[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_tmp6[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_tmp7[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_tmp8[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_tmp9[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_tmp10[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_tmp11[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_tmp12[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_tmp13[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_tmp14[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_tmp15[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_tmp16[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_tmp17[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_m1[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_x1[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_x2[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_1st_rel_error[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_t[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_last_rel_error[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_pole[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_type_pole[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_x2_init[term] := 0.0; term := term + 1; od;# end do number 2 ; term := 1; while term <= max_terms do # do number 2 array_x1_init[term] := 0.0; term := term + 1; od;# end do number 2 ; ord := 1; while ord <=2 do # do number 2 term := 1; while term <= 3 do # do number 3 array_complex_pole[ord,term] := 0.0; term := term + 1; od;# end do number 3 ; ord := ord + 1; od;# end do number 2 ; ord := 1; while ord <=3 do # do number 2 term := 1; while term <= max_terms do # do number 3 array_x2_higher[ord,term] := 0.0; term := term + 1; od;# end do number 3 ; ord := ord + 1; od;# end do number 2 ; ord := 1; while ord <=2 do # do number 2 term := 1; while term <= 3 do # do number 3 array_real_pole[ord,term] := 0.0; term := term + 1; od;# end do number 3 ; ord := ord + 1; od;# end do number 2 ; ord := 1; while ord <=2 do # do number 2 term := 1; while term <= 3 do # do number 3 array_poles[ord,term] := 0.0; term := term + 1; od;# end do number 3 ; ord := ord + 1; od;# end do number 2 ; ord := 1; while ord <=3 do # do number 2 term := 1; while term <= max_terms do # do number 3 array_x2_higher_work[ord,term] := 0.0; term := term + 1; od;# end do number 3 ; ord := ord + 1; od;# end do number 2 ; ord := 1; while ord <=2 do # do number 2 term := 1; while term <= max_terms do # do number 3 array_x1_higher_work2[ord,term] := 0.0; term := term + 1; od;# end do number 3 ; ord := ord + 1; od;# end do number 2 ; ord := 1; while ord <=2 do # do number 2 term := 1; while term <= max_terms do # do number 3 array_x1_higher[ord,term] := 0.0; term := term + 1; od;# end do number 3 ; ord := ord + 1; od;# end do number 2 ; ord := 1; while ord <=3 do # do number 2 term := 1; while term <= max_terms do # do number 3 array_x2_higher_work2[ord,term] := 0.0; term := term + 1; od;# end do number 3 ; ord := ord + 1; od;# end do number 2 ; ord := 1; while ord <=2 do # do number 2 term := 1; while term <= max_terms do # do number 3 array_x1_higher_work[ord,term] := 0.0; term := term + 1; od;# end do number 3 ; ord := ord + 1; od;# end do number 2 ; #BEGIN ARRAYS DEFINED AND INITIALIZATED array_tmp17 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_tmp17[term] := 0.0; term := term + 1; od;# end do number 2 ; array_tmp16 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_tmp16[term] := 0.0; term := term + 1; od;# end do number 2 ; array_tmp15 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_tmp15[term] := 0.0; term := term + 1; od;# end do number 2 ; array_tmp14 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_tmp14[term] := 0.0; term := term + 1; od;# end do number 2 ; array_tmp13 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_tmp13[term] := 0.0; term := term + 1; od;# end do number 2 ; array_tmp12 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_tmp12[term] := 0.0; term := term + 1; od;# end do number 2 ; array_tmp11 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_tmp11[term] := 0.0; term := term + 1; od;# end do number 2 ; array_tmp10 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_tmp10[term] := 0.0; term := term + 1; od;# end do number 2 ; array_tmp9 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_tmp9[term] := 0.0; term := term + 1; od;# end do number 2 ; array_tmp8 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_tmp8[term] := 0.0; term := term + 1; od;# end do number 2 ; array_tmp7 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_tmp7[term] := 0.0; term := term + 1; od;# end do number 2 ; array_tmp6 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_tmp6[term] := 0.0; term := term + 1; od;# end do number 2 ; array_tmp5 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_tmp5[term] := 0.0; term := term + 1; od;# end do number 2 ; array_tmp4 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_tmp4[term] := 0.0; term := term + 1; od;# end do number 2 ; array_tmp3 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_tmp3[term] := 0.0; term := term + 1; od;# end do number 2 ; array_tmp2 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_tmp2[term] := 0.0; term := term + 1; od;# end do number 2 ; array_tmp1 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_tmp1[term] := 0.0; term := term + 1; od;# end do number 2 ; array_tmp0 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_tmp0[term] := 0.0; term := term + 1; od;# end do number 2 ; array_x2 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_x2[term] := 0.0; term := term + 1; od;# end do number 2 ; array_x1 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_x1[term] := 0.0; term := term + 1; od;# end do number 2 ; array_t := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_t[term] := 0.0; term := term + 1; od;# end do number 2 ; array_const_4D0 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_const_4D0[term] := 0.0; term := term + 1; od;# end do number 2 ; array_const_4D0[1] := 4.0; array_const_2 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_const_2[term] := 0.0; term := term + 1; od;# end do number 2 ; array_const_2[1] := 2; array_const_1 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_const_1[term] := 0.0; term := term + 1; od;# end do number 2 ; array_const_1[1] := 1; array_const_2D0 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_const_2D0[term] := 0.0; term := term + 1; od;# end do number 2 ; array_const_2D0[1] := 2.0; array_const_3D0 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_const_3D0[term] := 0.0; term := term + 1; od;# end do number 2 ; array_const_3D0[1] := 3.0; array_const_0D0 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms + 1 do # do number 2 array_const_0D0[term] := 0.0; term := term + 1; od;# end do number 2 ; array_const_0D0[1] := 0.0; array_m1 := Array(1..(max_terms+1 + 1),[]); term := 1; while term <= max_terms do # do number 2 array_m1[term] := 0.0; term := term + 1; od;# end do number 2 ; array_m1[1] := -1.0; #END ARRAYS DEFINED AND INITIALIZATED #TOP SECOND INPUT BLOCK #BEGIN SECOND INPUT BLOCK #BEGIN SECOND INPUT BLOCK t_start := 0.5; t_end := 5.0; array_x1_init[1] := exact_soln_x1(t_start); array_x2_init[1] := exact_soln_x2(t_start); array_x2_init[2] := exact_soln_x2p(t_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 10; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.00005 ; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; #END OVERRIDE BLOCK #END SECOND INPUT BLOCK #BEGIN INITS AFTER SECOND INPUT BLOCK glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); glob_abserr := 10.0 ^ (glob_log10_abserr); glob_relerr := 10.0 ^ (glob_log10_relerr); chk_data(); #AFTER INITS AFTER SECOND INPUT BLOCK if glob_html_log then # if number 3 html_log_file := fopen("html/entry.html",WRITE,TEXT); fi;# end if 3 ; #BEGIN SOLUTION CODE omniout_str(ALWAYS,"START of Soultion"); #Start Series -- INITIALIZE FOR SOLUTION array_t[1] := t_start; array_t[2] := glob_h; order_diff := 1; #Start Series array_x1 term_no := 1; while (term_no <= order_diff) do # do number 2 array_x1[term_no] := array_x1_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); term_no := term_no + 1; od;# end do number 2 ; rows := order_diff; r_order := 1; while (r_order <= rows) do # do number 2 term_no := 1; while (term_no <= (rows - r_order + 1)) do # do number 3 it := term_no + r_order - 1; array_x1_higher[r_order,term_no] := array_x1_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); term_no := term_no + 1; od;# end do number 3 ; r_order := r_order + 1; od;# end do number 2 ; order_diff := 2; #Start Series array_x2 term_no := 1; while (term_no <= order_diff) do # do number 2 array_x2[term_no] := array_x2_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); term_no := term_no + 1; od;# end do number 2 ; rows := order_diff; r_order := 1; while (r_order <= rows) do # do number 2 term_no := 1; while (term_no <= (rows - r_order + 1)) do # do number 3 it := term_no + r_order - 1; array_x2_higher[r_order,term_no] := array_x2_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); term_no := term_no + 1; od;# end do number 3 ; r_order := r_order + 1; od;# end do number 2 ; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); start_array_x1(); if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 3 tmp := abs(array_x1_higher[1,1]); log10norm := (log10(tmp)); if (log10norm < glob_log10normmin) then # if number 4 glob_log10normmin := log10norm; fi;# end if 4 fi;# end if 3 ; display_alot(current_iter) ; start_array_x2(); if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 3 tmp := abs(array_x2_higher[1,1]); log10norm := (log10(tmp)); if (log10norm < glob_log10normmin) then # if number 4 glob_log10normmin := log10norm; fi;# end if 4 fi;# end if 3 ; display_alot(current_iter) ; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL," "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while ((glob_current_iter < glob_max_iter) and (array_t[1] <= t_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 #left paren 0001C omniout_str(INFO," "); omniout_str(INFO,"TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; sub_iter := 1; while sub_iter <= 3 do # do number 3 atomall() ; sub_iter := sub_iter + 1; od;# end do number 3 ; if (glob_look_poles) then # if number 3 #left paren 0004C check_for_pole(); fi;# end if 3 ;#was right paren 0004C array_t[1] := array_t[1] + glob_h; array_t[2] := glob_h; order_diff := 1; #Jump Series array_x1 #START PART 1 SUM AND ADJUST #START SUM AND ADJUST EQ =1 #sum_and_adjust array_x1 order_diff := 1; #BEFORE ADJUST SUBSERIES EQ =1 order_diff := 1; ord := 2; calc_term := 1; #adjust_subseriesarray_x1 iii := glob_max_terms; while (iii >= calc_term) do # do number 3 array_x1_higher_work[2,iii] := array_x1_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); iii := iii - 1; od;# end do number 3 ; #AFTER ADJUST SUBSERIES EQ =1 #BEFORE SUM SUBSERIES EQ =1 order_diff := 1; temp_sum := 0.0; ord := 2; calc_term := 1; #sum_subseriesarray_x1 iii := glob_max_terms; while (iii >= calc_term) do # do number 3 temp_sum := temp_sum + array_x1_higher_work[ord,iii]; iii := iii - 1; od;# end do number 3 ; array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); #AFTER SUM SUBSERIES EQ =1 #BEFORE ADJUST SUBSERIES EQ =1 order_diff := 1; ord := 1; calc_term := 2; #adjust_subseriesarray_x1 iii := glob_max_terms; while (iii >= calc_term) do # do number 3 array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); iii := iii - 1; od;# end do number 3 ; #AFTER ADJUST SUBSERIES EQ =1 #BEFORE SUM SUBSERIES EQ =1 order_diff := 1; temp_sum := 0.0; ord := 1; calc_term := 2; #sum_subseriesarray_x1 iii := glob_max_terms; while (iii >= calc_term) do # do number 3 temp_sum := temp_sum + array_x1_higher_work[ord,iii]; iii := iii - 1; od;# end do number 3 ; array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); #AFTER SUM SUBSERIES EQ =1 #BEFORE ADJUST SUBSERIES EQ =1 order_diff := 1; ord := 1; calc_term := 1; #adjust_subseriesarray_x1 iii := glob_max_terms; while (iii >= calc_term) do # do number 3 array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); iii := iii - 1; od;# end do number 3 ; #AFTER ADJUST SUBSERIES EQ =1 #BEFORE SUM SUBSERIES EQ =1 order_diff := 1; temp_sum := 0.0; ord := 1; calc_term := 1; #sum_subseriesarray_x1 iii := glob_max_terms; while (iii >= calc_term) do # do number 3 temp_sum := temp_sum + array_x1_higher_work[ord,iii]; iii := iii - 1; od;# end do number 3 ; array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); #AFTER SUM SUBSERIES EQ =1 #END SUM AND ADJUST EQ =1 #END PART 1 #START PART 2 MOVE TERMS to REGULAR Array term_no := glob_max_terms; while (term_no >= 1) do # do number 3 array_x1[term_no] := array_x1_higher_work2[1,term_no]; ord := 1; while ord <= order_diff do # do number 4 array_x1_higher[ord,term_no] := array_x1_higher_work2[ord,term_no]; ord := ord + 1; od;# end do number 4 ; term_no := term_no - 1; od;# end do number 3 ; #END PART 2 HEVE MOVED TERMS to REGULAR Array order_diff := 2; #Jump Series array_x2 #START PART 1 SUM AND ADJUST #START SUM AND ADJUST EQ =2 #sum_and_adjust array_x2 order_diff := 2; #BEFORE ADJUST SUBSERIES EQ =2 order_diff := 2; ord := 3; calc_term := 1; #adjust_subseriesarray_x2 iii := glob_max_terms; while (iii >= calc_term) do # do number 3 array_x2_higher_work[3,iii] := array_x2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); iii := iii - 1; od;# end do number 3 ; #AFTER ADJUST SUBSERIES EQ =2 #BEFORE SUM SUBSERIES EQ =2 order_diff := 2; temp_sum := 0.0; ord := 3; calc_term := 1; #sum_subseriesarray_x2 iii := glob_max_terms; while (iii >= calc_term) do # do number 3 temp_sum := temp_sum + array_x2_higher_work[ord,iii]; iii := iii - 1; od;# end do number 3 ; array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); #AFTER SUM SUBSERIES EQ =2 #BEFORE ADJUST SUBSERIES EQ =2 order_diff := 2; ord := 2; calc_term := 2; #adjust_subseriesarray_x2 iii := glob_max_terms; while (iii >= calc_term) do # do number 3 array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); iii := iii - 1; od;# end do number 3 ; #AFTER ADJUST SUBSERIES EQ =2 #BEFORE SUM SUBSERIES EQ =2 order_diff := 2; temp_sum := 0.0; ord := 2; calc_term := 2; #sum_subseriesarray_x2 iii := glob_max_terms; while (iii >= calc_term) do # do number 3 temp_sum := temp_sum + array_x2_higher_work[ord,iii]; iii := iii - 1; od;# end do number 3 ; array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); #AFTER SUM SUBSERIES EQ =2 #BEFORE ADJUST SUBSERIES EQ =2 order_diff := 2; ord := 2; calc_term := 1; #adjust_subseriesarray_x2 iii := glob_max_terms; while (iii >= calc_term) do # do number 3 array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); iii := iii - 1; od;# end do number 3 ; #AFTER ADJUST SUBSERIES EQ =2 #BEFORE SUM SUBSERIES EQ =2 order_diff := 2; temp_sum := 0.0; ord := 2; calc_term := 1; #sum_subseriesarray_x2 iii := glob_max_terms; while (iii >= calc_term) do # do number 3 temp_sum := temp_sum + array_x2_higher_work[ord,iii]; iii := iii - 1; od;# end do number 3 ; array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); #AFTER SUM SUBSERIES EQ =2 #BEFORE ADJUST SUBSERIES EQ =2 order_diff := 2; ord := 1; calc_term := 3; #adjust_subseriesarray_x2 iii := glob_max_terms; while (iii >= calc_term) do # do number 3 array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); iii := iii - 1; od;# end do number 3 ; #AFTER ADJUST SUBSERIES EQ =2 #BEFORE SUM SUBSERIES EQ =2 order_diff := 2; temp_sum := 0.0; ord := 1; calc_term := 3; #sum_subseriesarray_x2 iii := glob_max_terms; while (iii >= calc_term) do # do number 3 temp_sum := temp_sum + array_x2_higher_work[ord,iii]; iii := iii - 1; od;# end do number 3 ; array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); #AFTER SUM SUBSERIES EQ =2 #BEFORE ADJUST SUBSERIES EQ =2 order_diff := 2; ord := 1; calc_term := 2; #adjust_subseriesarray_x2 iii := glob_max_terms; while (iii >= calc_term) do # do number 3 array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); iii := iii - 1; od;# end do number 3 ; #AFTER ADJUST SUBSERIES EQ =2 #BEFORE SUM SUBSERIES EQ =2 order_diff := 2; temp_sum := 0.0; ord := 1; calc_term := 2; #sum_subseriesarray_x2 iii := glob_max_terms; while (iii >= calc_term) do # do number 3 temp_sum := temp_sum + array_x2_higher_work[ord,iii]; iii := iii - 1; od;# end do number 3 ; array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); #AFTER SUM SUBSERIES EQ =2 #BEFORE ADJUST SUBSERIES EQ =2 order_diff := 2; ord := 1; calc_term := 1; #adjust_subseriesarray_x2 iii := glob_max_terms; while (iii >= calc_term) do # do number 3 array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); iii := iii - 1; od;# end do number 3 ; #AFTER ADJUST SUBSERIES EQ =2 #BEFORE SUM SUBSERIES EQ =2 order_diff := 2; temp_sum := 0.0; ord := 1; calc_term := 1; #sum_subseriesarray_x2 iii := glob_max_terms; while (iii >= calc_term) do # do number 3 temp_sum := temp_sum + array_x2_higher_work[ord,iii]; iii := iii - 1; od;# end do number 3 ; array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); #AFTER SUM SUBSERIES EQ =2 #END SUM AND ADJUST EQ =2 #END PART 1 #START PART 2 MOVE TERMS to REGULAR Array term_no := glob_max_terms; while (term_no >= 1) do # do number 3 array_x2[term_no] := array_x2_higher_work2[1,term_no]; ord := 1; while ord <= order_diff do # do number 4 array_x2_higher[ord,term_no] := array_x2_higher_work2[ord,term_no]; ord := ord + 1; od;# end do number 4 ; term_no := term_no - 1; od;# end do number 3 ; #END PART 2 HEVE MOVED TERMS to REGULAR Array display_alot(current_iter) ; od;# end do number 2 ;#right paren 0001C omniout_str(ALWAYS,"Finished!"); if (glob_iter >= glob_max_iter) then # if number 3 omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") fi;# end if 3 ; if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3 omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") fi;# end if 3 ; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); omniout_str(INFO,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"); omniout_int(INFO,"Iterations ",32,glob_iter,4," ") ; prog_report(t_start,t_end); if glob_html_log then # if number 3 logstart(html_log_file); logitem_str(html_log_file,"2012-06-02T02:11:42-05:00") ; logitem_str(html_log_file,"Maple") ; logitem_str(html_log_file,"complicated2") ; logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;") ; logitem_float(html_log_file,t_start) ; logitem_float(html_log_file,t_end) ; logitem_float(html_log_file,array_t[1]) ; logitem_float(html_log_file,glob_h) ; logitem_integer(html_log_file,Digits) ; ; logitem_integer(html_log_file,glob_max_terms) ; logitem_float(html_log_file,array_1st_rel_error[1]) ; logitem_float(html_log_file,array_last_rel_error[1]) ; logitem_integer(html_log_file,glob_iter) ; logitem_pole(html_log_file,array_type_pole[1]) ; if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 4 logitem_float(html_log_file,array_pole[1]) ; logitem_float(html_log_file,array_pole[2]) ; 0; else logitem_str(html_log_file,"NA") ; logitem_str(html_log_file,"NA") ; 0; fi;# end if 4 ; logitem_time(html_log_file,convfloat(glob_clock_sec)) ; if glob_percent_done < 100.0 then # if number 4 logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file,"Done") ; 0 fi;# end if 4 ; log_revs(html_log_file," 076 ") ; logitem_str(html_log_file,"complicated2 diffeq.mxt") ; logitem_str(html_log_file,"complicated2 maple results") ; logitem_str(html_log_file,"sub iter tot order") ; logend(html_log_file) ; logditto(html_log_file) ; logditto(html_log_file) ; logditto(html_log_file) ; logitem_str(html_log_file,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;") ; logditto(html_log_file) ; logditto(html_log_file) ; logditto(html_log_file) ; logditto(html_log_file) ; logditto(html_log_file) ; ; logditto(html_log_file) ; logitem_float(html_log_file,array_1st_rel_error[2]) ; logitem_float(html_log_file,array_last_rel_error[2]) ; logditto(html_log_file) ; logitem_pole(html_log_file,array_type_pole[2]) ; if array_type_pole[2] = 1 or array_type_pole[2] = 2 then # if number 4 logitem_float(html_log_file,array_pole[1]) ; logitem_float(html_log_file,array_pole[2]) ; 0; else logitem_str(html_log_file,"NA") ; logitem_str(html_log_file,"NA") ; 0; fi;# end if 4 ; logditto(html_log_file) ; if glob_percent_done < 100.0 then # if number 4 logditto(html_log_file) ; 0 else logditto(html_log_file) ; 0 fi;# end if 4 ; logditto(html_log_file); ; logditto(html_log_file) ; logditto(html_log_file) ; logditto(html_log_file) ; logend(html_log_file) ; ; fi;# end if 3 ; if glob_html_log then # if number 3 fclose(html_log_file); fi;# end if 3 ; ;; #END OUTFILEMAIN # End Function number 8 end; mainprog();