##############ECHO OF PROBLEM################# ##############temp/lin_arcsinpostode.ode################# diff ( y , x , 1 ) = arcsin ( 0.1 * x + 0.2 ) ; ! // BEGIN FIRST INPUT BLOCK max_terms=30; Digits=32; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=-0.8; x_end=0.8; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=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 double exact_soln_y (double x) { return(10.0 * (0.1 * x + 0.2) * arcsin(0.1 * x + 0.2 ) + 10.0 * sqrt(1.0 - expt((0.1 * x + 0.2) , 2 ))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1.6 estimated_steps = 1600000 step_error = 2.635231383473649e-21 est_needed_step_err = 2.635231383473649e-21 opt_iter = 1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 10.07208677566643 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 10.07208677566643 desired_abs_gbl_error = 1.007208677566643e-15 range = 1.6 estimated_steps = 1600000 step_error = 2.65422791683061e-20 est_needed_step_err = 2.65422791683061e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 2 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 10.07208677566643 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 10.07208677566643 desired_abs_gbl_error = 1.007208677566643e-15 range = 1.6 estimated_steps = 800000.0000000001 step_error = 3.753645117611135e-20 est_needed_step_err = 3.753645117611135e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 3 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 10.07208677566643 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 10.07208677566643 desired_abs_gbl_error = 1.007208677566643e-15 range = 1.6 estimated_steps = 400000.0000000001 step_error = 5.308455833661219e-20 est_needed_step_err = 5.308455833661219e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 4 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 10.07208677566643 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 10.07208677566643 desired_abs_gbl_error = 1.007208677566643e-15 range = 1.6 estimated_steps = 200000 step_error = 7.50729023522227e-20 est_needed_step_err = 7.50729023522227e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 5 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 10.07208677566643 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 10.07208677566643 desired_abs_gbl_error = 1.007208677566643e-15 range = 1.6 estimated_steps = 100000 step_error = 1.061691166732244e-19 est_needed_step_err = 1.061691166732244e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 6 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 10.07208677566643 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 10.07208677566643 desired_abs_gbl_error = 1.007208677566643e-15 range = 1.6 estimated_steps = 50000.00000000001 step_error = 1.501458047044454e-19 est_needed_step_err = 1.501458047044454e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 7 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 10.07208677566643 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 10.07208677566643 desired_abs_gbl_error = 1.007208677566643e-15 range = 1.6 estimated_steps = 25000 step_error = 2.123382333464488e-19 est_needed_step_err = 2.123382333464488e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 8 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 10.07208677566643 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 10.07208677566643 desired_abs_gbl_error = 1.007208677566643e-15 range = 1.6 estimated_steps = 12500 step_error = 3.002916094088908e-19 est_needed_step_err = 3.002916094088908e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 9 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 10.07208677566643 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 10.07208677566643 desired_abs_gbl_error = 1.007208677566643e-15 range = 1.6 estimated_steps = 6250.000000000001 step_error = 4.246764666928975e-19 est_needed_step_err = 4.246764666928975e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 10 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 10.07208677566643 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 10.07208677566643 desired_abs_gbl_error = 1.007208677566643e-15 range = 1.6 estimated_steps = 3125 step_error = 6.005832188177816e-19 est_needed_step_err = 6.005832188177816e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 11 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 10.07208677566643 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 10.07208677566643 desired_abs_gbl_error = 1.007208677566643e-15 range = 1.6 estimated_steps = 1562.5 step_error = 8.493529333857951e-19 est_needed_step_err = 8.493529333857951e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 12 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 10.07208677566643 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 10.07208677566643 desired_abs_gbl_error = 1.007208677566643e-15 range = 1.6 estimated_steps = 781.2500000000001 step_error = 1.201166437635563e-18 est_needed_step_err = 1.201166437635563e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 13 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 10.07208677566643 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 10.07208677566643 desired_abs_gbl_error = 1.007208677566643e-15 range = 1.6 estimated_steps = 390.6250000000001 step_error = 1.69870586677159e-18 est_needed_step_err = 1.69870586677159e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 14 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 10.07208677566643 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 10.07208677566643 desired_abs_gbl_error = 1.007208677566643e-15 range = 1.6 estimated_steps = 195.3125 step_error = 2.402332875271126e-18 est_needed_step_err = 2.402332875271126e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 15 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 10.07208677566643 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 10.07208677566643 desired_abs_gbl_error = 1.007208677566643e-15 range = 1.6 estimated_steps = 97.65625000000001 step_error = 3.39741173354318e-18 est_needed_step_err = 3.39741173354318e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 16 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 10.07208677566643 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 10.07208677566643 desired_abs_gbl_error = 1.007208677566643e-15 range = 1.6 estimated_steps = 48.82812500000001 step_error = 4.804665750542253e-18 est_needed_step_err = 4.804665750542253e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 17 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 10.07208677566643 glob_desired_digits_correct = 16 estimated_h = 0.065536 estimated_answer = 10.07208677566643 desired_abs_gbl_error = 1.007208677566643e-15 range = 1.6 estimated_steps = 24.4140625 step_error = 6.794823467086361e-18 est_needed_step_err = 6.794823467086361e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = -0.8 y[1] (closed_form) = 10.07208677566643 y[1] (numeric) = 10.07208677566643 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7000000000000001 y[1] (closed_form) = 10.08461961211218 y[1] (numeric) = 10.08461940325843 absolute error = 2.088537573996518e-07 relative error = 2.07101274448475e-06 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 8 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6000000000000001 y[1] (closed_form) = 10.09816101618305 y[1] (numeric) = 10.09816058054613 absolute error = 4.356369203151189e-07 relative error = 4.314022321658157e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5000000000000001 y[1] (closed_form) = 10.11271237580762 y[1] (numeric) = 10.11271169524414 absolute error = 6.805634793494164e-07 relative error = 6.729781823692628e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4000000000000001 y[1] (closed_form) = 10.12827518812551 y[1] (numeric) = 10.12827424425924 absolute error = 9.438662740279824e-07 relative error = 9.3191215334925e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3000000000000002 y[1] (closed_form) = 10.14485106091358 y[1] (numeric) = 10.14484983511597 absolute error = 1.225797609194501e-06 relative error = 1.208295323247568e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2000000000000001 y[1] (closed_form) = 10.16244171413014 y[1] (numeric) = 10.16244018750017 absolute error = 1.526629962000925e-06 relative error = 1.502227520654074e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1000000000000001 y[1] (closed_form) = 10.18104898158115 y[1] (numeric) = 10.18104713492443 absolute error = 1.846656724424633e-06 relative error = 1.813817738982964e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.387778780781446e-16 y[1] (closed_form) = 10.20067481271337 y[1] (numeric) = 10.20067262652033 absolute error = 2.186193043485218e-06 relative error = 2.143184724171883e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09999999999999987 y[1] (closed_form) = 10.22132127453915 y[1] (numeric) = 10.22131872896244 absolute error = 2.545576705870189e-06 relative error = 2.490457581263106e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1999999999999999 y[1] (closed_form) = 10.24299055369871 y[1] (numeric) = 10.24298762852958 absolute error = 2.925169125589377e-06 relative error = 2.855776455376218e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2999999999999999 y[1] (closed_form) = 10.26568495866573 y[1] (numeric) = 10.26568163330933 absolute error = 3.32535640268361e-06 relative error = 3.239293253273399e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3999999999999999 y[1] (closed_form) = 10.28940692210279 y[1] (numeric) = 10.28940317555231 absolute error = 3.746550477856658e-06 relative error = 3.641172427352107e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4999999999999999 y[1] (closed_form) = 10.31415900337374 y[1] (numeric) = 10.31415481418335 absolute error = 4.189190388359521e-06 relative error = 4.061591824393289e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5999999999999999 y[1] (closed_form) = 10.33994389122067 y[1] (numeric) = 10.33993923747705 absolute error = 4.653743616245265e-06 relative error = 4.500743587396656e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6999999999999998 y[1] (closed_form) = 10.3667644066138 y[1] (numeric) = 10.36675926590623 absolute error = 5.14070756629792e-06 relative error = 4.958835143411039e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7999999999999998 y[1] (closed_form) = 10.39462350578332 y[1] (numeric) = 10.39461785517215 absolute error = 5.650611166529984e-06 relative error = 5.436090266651909e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = arcsin ( 0.1 * x + 0.2 ) ; Iterations = 17 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 112.5 %