##############ECHO OF PROBLEM################# ##############temp/mtest7_sm_hpostode.ode################# diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * y2 ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.0 x_end=5.0 $array_y1_init[0 + 1] = exact_soln_y1(x_start) $array_y2_init[0 + 1] = exact_soln_y2(x_start) $array_y2_init[1 + 1] = exact_soln_y2p(x_start) $array_y2_init[2 + 1] = exact_soln_y2pp(x_start) $array_y2_init[4 + 1] = exact_soln_y2pppp(x_start) $glob_look_poles=true $glob_max_iter=20 $glob_max_h=0.000001 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.001 $glob_look_poles=true $glob_max_iter=10000000 $glob_max_minutes=3 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y1 (x) return( cos(x)) end def exact_soln_y2 (x) return( sin(x)) end def exact_soln_y2p (x) return( cos(x)) end def exact_soln_y2pp (x) return( -sin(x)) end def exact_soln_y2ppp (x) return( -cos(x)) end def exact_soln_y2pppp (x) return( sin(x)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 opt_iter 1 $glob_desired_digits_correct 10 desired_abs_gbl_error 1.0e-10 range 5.0 estimated_steps 5000000.0 step_error 2.0e-17 est_needed_step_err 2.0e-17 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 value3 2.4795962632247947e-183 max_value3 2.4795962632247947e-183 value3 2.4795962632247947e-183 best_h 1.0e-06 START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y2[1] (analytic) 0.0 y2[1] (numeric) 0.0 absolute error 0.0 relative error -1.0% Correct digits -1 h 1.0e-06 y1[1] (analytic) 1.0 y1[1] (numeric) 1.0 absolute error 0.0 relative error 0.0% Correct digits 16 h 1.0e-06 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] 0.0010000000000000152 y2[1] (analytic) 0.0009999998333333569 y2[1] (numeric) 0.0010000000000000187 absolute error 1.6666666180845113e-10 relative error 1.666666895862288e-05% Correct digits 6 h 1.0e-06 y1[1] (analytic) 0.9999995000000417 y1[1] (numeric) 0.9999994999999997 absolute error 4.196643033083092e-14 relative error 4.196645131405483e-12% Correct digits 13 h 1.0e-06 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] 0.002000999999999941 y2[1] (analytic) 0.002000998664665875 y2[1] (numeric) 0.0020010000000002808 absolute error 1.3353344055500038e-09 relative error 6.673339813412502e-05% Correct digits 6 h 1.0e-06 y1[1] (analytic) 0.999997998000168 y1[1] (numeric) 0.9999979979994993 absolute error 6.686873277317318e-13 relative error 6.686886664463297e-11% Correct digits 12 h 1.0e-06 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] 0.003000000000000074 y2[1] (analytic) 0.002999995500002099 y2[1] (numeric) 0.0030000000000020184 absolute error 4.499999919568842e-09 relative error 0.00015000022231918995% Correct digits 5 h 1.0e-06 y1[1] (analytic) 0.999995500003375 y1[1] (numeric) 0.9999954999999998 absolute error 3.3751890171629384e-12 relative error 3.375204205570472e-10% Correct digits 11 h 1.0e-06 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] 0.0040000000000002065 y2[1] (analytic) 0.003999989333342073 y2[1] (numeric) 0.004000000000008515 absolute error 1.0666666441609685e-08 relative error 0.00026666737215265185% Correct digits 5 h 1.0e-06 y1[1] (analytic) 0.9999920000106667 y1[1] (numeric) 0.999992 absolute error 1.0666689753691116e-11 relative error 1.066677508777804e-09% Correct digits 10 h 1.0e-06 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] 0.005000000000000339 y2[1] (analytic) 0.004999979166693047 y2[1] (numeric) 0.005000000000026009 absolute error 2.0833332961545104e-08 relative error 0.00041666839534701763% Correct digits 5 h 1.0e-06 y1[1] (analytic) 0.9999875000260416 y1[1] (numeric) 0.9999874999999996 absolute error 2.6042057399422447e-11 relative error 2.6042382928530867e-09% Correct digits 10 h 1.0e-06 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] 0.006000000000000472 y2[1] (analytic) 0.0059999640000652716 y2[1] (numeric) 0.00600000000006475 absolute error 3.599999947884874e-08 relative error 0.0006000035913291665% Correct digits 5 h 1.0e-06 y1[1] (analytic) 0.999982000054 y1[1] (numeric) 0.9999819999999996 absolute error 5.4000359739347914e-11 relative error 5.4001331760403536e-09% Correct digits 10 h 1.0e-06 NO POLE for equation 1 NO POLE for equation 2 Finished! Maximum Time Reached before Solution Completed! diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * y2 ; Iterations 6018 Total Elapsed Time 3 Minutes 0.0 Seconds Elapsed Time(since restart) 3 Minutes 0.0 Seconds Expected Time Remaining 1 Days 17 Hours 29 Minutes 6.499418496270664 Seconds Optimized Time Remaining 1 Days 17 Hours 29 Minutes 6.499418496270664 Seconds Expected Total Time 1 Days 17 Hours 32 Minutes 6.499418496270664 Seconds Time to Timeout 0.0 Seconds Percent Done 0.12038000000000948%