##############ECHO OF PROBLEM################# ##############temp/mtest2postode.ode################# diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 1 ) = y1 ; ! // BEGIN FIRST INPUT BLOCK Digits=64; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.2; x_end=0.8; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); glob_max_h=0.00001; glob_look_poles=true; glob_type_given_pole=3; // 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_y1 (double x) { return(cos(x)); } double exact_soln_y2 (double x) { return(sin(x)); } // 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 = 0.6000000000000001 estimated_steps = 600000.0000000001 step_error = 3.227486121839513e-21 est_needed_step_err = 3.227486121839513e-21 opt_iter = 1 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.9800665778412416 min_size = 0.1986693307950612 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.6000000000000001 estimated_steps = 600000.0000000001 step_error = 3.227486121839513e-21 est_needed_step_err = 3.227486121839513e-21 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 POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.9800665778412416 min_size = 0.1986693307950612 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.6000000000000001 estimated_steps = 300000.0000000001 step_error = 4.564354645876384e-21 est_needed_step_err = 4.564354645876384e-21 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 POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.9800665778412416 min_size = 0.1986693307950612 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.6000000000000001 estimated_steps = 150000 step_error = 6.454972243679027e-21 est_needed_step_err = 6.454972243679027e-21 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 POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.9800665778412416 min_size = 0.1986693307950612 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.6000000000000001 estimated_steps = 75000.00000000001 step_error = 9.128709291752767e-21 est_needed_step_err = 9.128709291752767e-21 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 SETTING H FOR MAX H NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.2 y1[1] (closed_form) = 0.9800665778412416 y1[1] (numeric) = 0.9800665778412416 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 1e-05 y2[1] (closed_form) = 0.1986693307950612 y2[1] (numeric) = 0.1986693307950612 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 1e-05 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.26000000000006 y1[1] (closed_form) = 0.9663899781344978 y1[1] (numeric) = 0.9681464179933859 absolute error = 0.00175643985888807 relative error = 0.1817526980441861 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 3 h = 1e-05 y2[1] (closed_form) = 0.2570805518922131 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.05841122109715186 relative error = 22.72098012363148 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 2 h = 1e-05 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.32000000000012 y1[1] (closed_form) = 0.9492354180824031 y1[1] (numeric) = 0.9562262581455301 absolute error = 0.006990840063127002 relative error = 0.73647062993599 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 1e-05 y2[1] (closed_form) = 0.3145665606162317 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1158972298211705 relative error = 36.84346791156992 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 2 h = 1e-05 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.38000000000018 y1[1] (closed_form) = 0.9286646355764435 y1[1] (numeric) = 0.9443060982976743 absolute error = 0.01564146272123079 relative error = 1.684296151917293 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 1e-05 y2[1] (closed_form) = 0.3709204694131499 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1722511386180887 relative error = 46.43883334090863 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 2 h = 1e-05 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.44000000000024 y1[1] (closed_form) = 0.9047516632198612 y1[1] (numeric) = 0.9323859384498185 absolute error = 0.02763427522995732 relative error = 3.054349204688004 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 1e-05 y2[1] (closed_form) = 0.4259394650662168 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2272701342711556 relative error = 53.35737890261566 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 2 h = 1e-05 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5000000000003 y1[1] (closed_form) = 0.8775825618902289 y1[1] (numeric) = 0.9204657786019628 absolute error = 0.0428832167117339 relative error = 4.88651650271714 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 1e-05 y2[1] (closed_form) = 0.4794255386044662 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.280756207809405 relative error = 58.560962068613 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 2 h = 1e-05 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5600000000000269 y1[1] (closed_form) = 0.8472551110134018 y1[1] (numeric) = 0.908545618754107 absolute error = 0.06129050774070521 relative error = 7.234008617238748 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 1e-05 y2[1] (closed_form) = 0.5311861979209063 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3325168671258451 relative error = 62.59892829055715 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 2 h = 1e-05 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6199999999997539 y1[1] (closed_form) = 0.813878456662677 y1[1] (numeric) = 0.8966254589062512 absolute error = 0.08274700224357423 relative error = 10.16699748791481 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 2 h = 1e-05 y2[1] (closed_form) = 0.5810351605371048 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3823658297420436 relative error = 65.80769215215605 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 2 h = 1e-05 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6799999999994808 y1[1] (closed_form) = 0.7775727187512544 y1[1] (numeric) = 0.8847052990583955 absolute error = 0.107132580307141 relative error = 13.77782138231276 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 2 h = 1e-05 y2[1] (closed_form) = 0.6287930240180648 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.4301236932230036 relative error = 68.40465412202894 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 2 h = 1e-05 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7399999999992077 y1[1] (closed_form) = 0.7384685587301221 y1[1] (numeric) = 0.8727851392105397 absolute error = 0.1343165804804176 relative error = 18.188530695388 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 2 h = 1e-05 y2[1] (closed_form) = 0.67428791162756 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.4756185808324987 relative error = 70.53642407506256 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 2 h = 1e-05 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7999999999989347 y1[1] (closed_form) = 0.6967067093479297 y1[1] (numeric) = 0.8608649793626839 absolute error = 0.1641582700147542 relative error = 23.56203375282481 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 2 h = 1e-05 y2[1] (closed_form) = 0.7173560908987805 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.5186867601037193 relative error = 72.30533993986906 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 2 h = 1e-05 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 1 ) = y1 ; Iterations = 60001 Total Elapsed Time = 13.0 Seconds Elapsed Time(since restart) = 13.0 Seconds Time to Timeout = 2 Minutes 47.0 Seconds Percent Done = 100 %