##############ECHO OF PROBLEM################# ##############temp/arcsin_sqrtpostode.ode################# diff ( y , x , 1 ) = arcsin ( sqrt ( 0.1 * x + 0.2 ) ) ; ! #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=0.5 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=0.01 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=-2.0 # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=0.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=0.5 # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=0.0 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=16 $glob_max_minutes=3.0 $glob_subiter_method=3 $glob_max_iter=100000000 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(10.0 * (0.1 * x + 0.2) * arcsin(sqrt ( 0.1 * x + 0.2)) + 5.0 * sqrt( 0.1 * x + 0.2) * sqrt( 0.8 - 0.1 * x) - 5.0 * arcsin(sqrt( 0.1 * x + 0.2))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.5 estimated_steps 500000.0 step_error 4.7140452079103165e-21 est_needed_step_err 4.7140452079103165e-21 opt_iter 1 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.609057172997582 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.5 estimated_steps 500000.0 step_error 4.7140452079103165e-21 est_needed_step_err 4.7140452079103165e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2587599705259397e-168 estimated_step_error 1.2587599705259397e-168 Double H and LOOP opt_iter 2 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.609057172997582 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.5 estimated_steps 250000.0 step_error 6.6666666666666666e-21 est_needed_step_err 6.6666666666666666e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.44739325058823e-161 estimated_step_error 8.44739325058823e-161 Double H and LOOP opt_iter 3 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.609057172997582 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.5 estimated_steps 125000.0 step_error 9.428090415820633e-21 est_needed_step_err 9.428090415820633e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.668947075830024e-153 estimated_step_error 5.668947075830024e-153 Double H and LOOP opt_iter 4 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.609057172997582 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.5 estimated_steps 62500.0 step_error 1.3333333333333333e-20 est_needed_step_err 1.3333333333333333e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.804362530936719e-145 estimated_step_error 3.804362530936719e-145 Double H and LOOP opt_iter 5 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.609057172997582 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.5 estimated_steps 31250.0 step_error 1.8856180831641266e-20 est_needed_step_err 1.8856180831641266e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.553059843214273e-137 estimated_step_error 2.553059843214273e-137 Double H and LOOP opt_iter 6 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.609057172997582 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.5 estimated_steps 15625.0 step_error 2.6666666666666666e-20 est_needed_step_err 2.6666666666666666e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.7133232387560482e-129 estimated_step_error 1.7133232387560482e-129 Double H and LOOP opt_iter 7 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.609057172997582 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.5 estimated_steps 7812.5 step_error 3.771236166328253e-20 est_needed_step_err 3.771236166328253e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.14978341491193e-121 estimated_step_error 1.14978341491193e-121 Double H and LOOP opt_iter 8 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.609057172997582 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.5 estimated_steps 3906.25 step_error 5.333333333333333e-20 est_needed_step_err 5.333333333333333e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.71595384942909e-114 estimated_step_error 7.71595384942909e-114 Double H and LOOP opt_iter 9 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.609057172997582 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.000256 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.5 estimated_steps 1953.125 step_error 7.542472332656506e-20 est_needed_step_err 7.542472332656506e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.177938614013485e-106 estimated_step_error 5.177938614013485e-106 Double H and LOOP opt_iter 10 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.609057172997582 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.000512 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.5 estimated_steps 976.5625 step_error 1.0666666666666666e-19 est_needed_step_err 1.0666666666666666e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.474653988869495e-98 estimated_step_error 3.474653988869495e-98 Double H and LOOP opt_iter 11 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.609057172997582 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.001024 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.5 estimated_steps 488.28125 step_error 1.5084944665313013e-19 est_needed_step_err 1.5084944665313013e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.331530024410956e-90 estimated_step_error 2.331530024410956e-90 Double H and LOOP opt_iter 12 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.609057172997582 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.002048 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.5 estimated_steps 244.140625 step_error 2.1333333333333333e-19 est_needed_step_err 2.1333333333333333e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.5642999847570358e-82 estimated_step_error 1.5642999847570358e-82 Double H and LOOP opt_iter 13 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.609057172997582 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.004096 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.5 estimated_steps 122.0703125 step_error 3.0169889330626025e-19 est_needed_step_err 3.0169889330626025e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0492966389250003e-74 estimated_step_error 1.0492966389250003e-74 Double H and LOOP opt_iter 14 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.609057172997582 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.008192 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.5 estimated_steps 61.03515625 step_error 4.2666666666666666e-19 est_needed_step_err 4.2666666666666666e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.03517910716513e-67 estimated_step_error 7.03517910716513e-67 Double H and LOOP opt_iter 15 SETTING H FOR MAX H Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.220837655125974 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y[1] (closed_form) 0.609057172997582 y[1] (numeric) 0.609057172997582 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0002204141583992 Order of pole (three term test) 1.4951455387822794 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.05 y[1] (closed_form) 0.6323953205685546 y[1] (numeric) 0.6323953140709647 absolute error 6.497589910559043e-09 relative error 1.027456987619293e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.01 Radius of convergence (given) for eq 1 2.05 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.050232285172133 Order of pole (three term test) 1.4950080683238043 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.09999999999999999 y[1] (closed_form) 0.6560431130637943 y[1] (numeric) 0.6560431000865576 absolute error 1.2977236618638699e-08 relative error 1.978107285972954e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.01 Radius of convergence (given) for eq 1 2.1 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.100244506250862 Order of pole (three term test) 1.4948697094385628 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.15 y[1] (closed_form) 0.6799978081605684 y[1] (numeric) 0.6799977887193155 absolute error 1.9441252940843867e-08 relative error 2.859017000868507e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.01 Radius of convergence (given) for eq 1 2.15 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1502570805794186 Order of pole (three term test) 1.4947304538002661 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.20000000000000004 y[1] (closed_form) 0.7042567802094295 y[1] (numeric) 0.7042567543175777 absolute error 2.589185177370723e-08 relative error 3.676478878344288e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.01 Radius of convergence (given) for eq 1 2.2 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.200270011378585 Order of pole (three term test) 1.4945902929758685 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.25000000000000006 y[1] (closed_form) 0.7288175137877979 y[1] (numeric) 0.7288174814566396 absolute error 3.233115830614253e-08 relative error 4.436111604688474e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.01 Radius of convergence (given) for eq 1 2.25 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2502833019052257 Order of pole (three term test) 1.494449218427039 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3000000000000001 y[1] (closed_form) 0.7536775977668664 y[1] (numeric) 0.7536775590056521 absolute error 3.876121423829204e-08 relative error 5.1429436609421386e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.01 Radius of convergence (given) for eq 1 2.3000000000000003 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3002969554532355 Order of pole (three term test) 1.494307221504636 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.35000000000000014 y[1] (closed_form) 0.7788347198413588 y[1] (numeric) 0.7788346746573727 absolute error 4.518398610819929e-08 relative error 5.801485855356171e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.01 Radius of convergence (given) for eq 1 2.35 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3503109753535387 Order of pole (three term test) 1.4941642934516899 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4000000000000002 y[1] (closed_form) 0.8042866614776245 y[1] (numeric) 0.8042866098762478 absolute error 5.1601376727106185e-08 relative error 6.415794168748844e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.01 Radius of convergence (given) for eq 1 2.4000000000000004 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.4003253649748606 Order of pole (three term test) 1.4940204253991154 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.45000000000000023 y[1] (closed_form) 0.8300312932406859 y[1] (numeric) 0.8300312352254611 absolute error 5.8015224846386104e-08 relative error 6.989522602199446e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.01 Radius of convergence (given) for eq 1 2.45 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.4503401277239396 Order of pole (three term test) 1.4938756083670441 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = arcsin ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations 50 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 102.00000000000004%