##############ECHO OF PROBLEM################# ##############temp/mtest4postode.ode################# diff ( y2 , x , 3 ) = m1 * cos(x) ; diff ( y1 , x , 1 ) = m1 * y2 + 1.0; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.1; x_end=5.0; glob_h=0.00001; 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); glob_max_iter=20; // 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; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y2 (double x) { return(1.0 + cos(x)); } double exact_soln_y2p (double x) { return( -sin(x)); } double exact_soln_y2pp (double x) { return( -cos(x)); } double exact_soln_y1 (double x) { return( 1.0 - sin(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 4.9 estimated_steps = 4900 step_error = 2.040816326530612e-14 est_needed_step_err = 2.040816326530612e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 6.025700482112569e-98 value3 = 3.17621306935755e-94 max_value3 = 3.17621306935755e-94 value3 = 3.17621306935755e-94 best_h = 0.001 START of Soultion x[1] = 0.1 y2[1] (analytic) = 1.995004165278026 y2[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 y1[1] (analytic) = 0.9001665833531718 y1[1] (numeric) = 0.9001665833531718 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 x[1] = 0.1 y2[1] (analytic) = 1.995004165278026 y2[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 y1[1] (analytic) = 0.9001665833531718 y1[1] (numeric) = 0.9001665833531718 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.101 y2[1] (analytic) = 1.994903834375977 y2[1] (numeric) = 1.994903834193466 absolute error = 1.825102291519443e-10 relative error = 9.148823417296957e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 0.899171629270432 y1[1] (numeric) = 0.8991716292704776 absolute error = 4.551914400963142e-14 relative error = 5.062342107764748e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.102 y2[1] (analytic) = 1.994802508570176 y2[1] (numeric) = 1.994802507109796 absolute error = 1.460380039119968e-09 relative error = 7.320925419162079e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 0.8981767760160545 y1[1] (numeric) = 0.8981767760167846 absolute error = 7.300826609935029e-13 relative error = 8.12849631040174e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.103 y2[1] (analytic) = 1.99470018796195 y2[1] (numeric) = 1.994700183032162 absolute error = 4.929788133267721e-09 relative error = 2.471443158735873e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 0.8971820245848925 y1[1] (numeric) = 0.8971820245885893 absolute error = 3.696820627396846e-12 relative error = 4.120480043174392e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.104 y2[1] (analytic) = 1.994596872653619 y2[1] (numeric) = 1.994596860965812 absolute error = 1.168780672244907e-08 relative error = 5.859733805207249e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 0.8961873759716973 y1[1] (numeric) = 0.8961873759833832 absolute error = 1.168587449029701e-11 relative error = 1.303954374231898e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.105 y2[1] (analytic) = 1.994492562748498 y2[1] (numeric) = 1.994492539916098 absolute error = 2.283239952660665e-08 relative error = 1.144772357292855e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 0.8951928311711175 y1[1] (numeric) = 0.8951928311996522 absolute error = 2.853473013431085e-11 relative error = 3.187551233735963e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.106 y2[1] (analytic) = 1.994387258350897 y2[1] (numeric) = 1.994387218888475 absolute error = 3.946242133068267e-08 relative error = 1.978673959405108e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 0.8941983911776978 y1[1] (numeric) = 0.8941983912368769 absolute error = 5.917910606001442e-11 relative error = 6.618118154079094e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.107 y2[1] (analytic) = 1.99428095956612 y2[1] (numeric) = 1.994280896888504 absolute error = 6.267761598621746e-08 relative error = 3.142867893591771e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 0.8932040569858781 y1[1] (numeric) = 0.8932040570955326 absolute error = 1.096545076961775e-10 relative error = 1.227653489015793e-08 % Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.108 y2[1] (analytic) = 1.994173666500467 y2[1] (numeric) = 1.99417357292185 absolute error = 9.357861685543867e-08 relative error = 4.692601172477511e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 0.8922098295899925 y1[1] (numeric) = 0.8922098297770888 absolute error = 1.870963384220659e-10 relative error = 2.096999295648249e-08 % Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.109 y2[1] (analytic) = 1.99406537926123 y2[1] (numeric) = 1.994065245994286 absolute error = 1.332669443687706e-07 relative error = 6.683178282657107e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 0.8912157099842684 y1[1] (numeric) = 0.8912157102840093 absolute error = 2.997408987681638e-10 relative error = 3.363281138451372e-08 % Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.11 y2[1] (analytic) = 1.993956097956697 y2[1] (numeric) = 1.993955915111692 absolute error = 1.828450046925667e-07 relative error = 9.169961408876395e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 0.8902216991628252 y1[1] (numeric) = 0.8902216996197519 absolute error = 4.569267186838033e-10 relative error = 5.132729511238633e-08 % Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.111 y2[1] (analytic) = 1.993845822696148 y2[1] (numeric) = 1.993845579280058 absolute error = 2.434160901731985e-07 relative error = 1.220837074774632e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 0.8892277981196737 y1[1] (numeric) = 0.8892277987887689 absolute error = 6.690952236709791e-10 relative error = 7.524452396627969e-08 % Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.112 y2[1] (analytic) = 1.99373455358986 y2[1] (numeric) = 1.993734237505483 absolute error = 3.160843773386546e-07 relative error = 1.585388469942111e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 0.8882340078487148 y1[1] (numeric) = 0.8882340087965062 absolute error = 9.477914009181632e-10 relative error = 1.067051466779228e-07 % Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.113 y2[1] (analytic) = 1.993622290749101 y2[1] (numeric) = 1.993621888794176 absolute error = 4.019549249001386e-07 relative error = 2.016204005970983e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 0.8872403293437388 y1[1] (numeric) = 0.8872403306494036 absolute error = 1.305664798501027e-09 relative error = 1.471602175102638e-07 % Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.114 y2[1] (analytic) = 1.993509034286134 y2[1] (numeric) = 1.99350853215246 absolute error = 5.021336746402483e-07 relative error = 2.518843235742144e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 0.886246763598424 y1[1] (numeric) = 0.8862467653548947 absolute error = 1.756470635605467e-09 relative error = 1.981920507640194e-07 % Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.115 y2[1] (analytic) = 1.993394784314216 y2[1] (numeric) = 1.993394166586768 absolute error = 6.177274483043504e-07 relative error = 3.098871599169284e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 0.8852533116063361 y1[1] (numeric) = 0.8852533139214066 absolute error = 2.315070468661418e-09 relative error = 2.615150305917079e-07 % Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.116 y2[1] (analytic) = 1.993279540947596 y2[1] (numeric) = 1.993278791103648 absolute error = 7.49843947822626e-07 relative error = 3.761860453683048e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 0.8842599743609272 y1[1] (numeric) = 0.8842599773583603 absolute error = 2.997433079521272e-09 relative error = 3.389764510926302e-07 % Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.117 y2[1] (analytic) = 1.993163304301518 y2[1] (numeric) = 1.993162404709764 absolute error = 8.99591753977802e-07 relative error = 4.513387096964712e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 0.8832667528555341 y1[1] (numeric) = 0.8832667566761696 absolute error = 3.820635474660605e-09 relative error = 4.325573743502495e-07 % Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.118 y2[1] (analytic) = 1.993046074492218 y2[1] (numeric) = 1.993045006411893 absolute error = 1.068080324628795e-06 relative error = 5.359034787496909e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 0.8822736480833785 y1[1] (numeric) = 0.882273652886242 absolute error = 4.802863551311987e-09 relative error = 5.44373456211184e-07 % Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.119 y2[1] (analytic) = 1.992927851636927 y2[1] (numeric) = 1.992926595216932 absolute error = 1.256419994266622e-06 relative error = 6.304392771843893e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 0.8812806610375651 y1[1] (numeric) = 0.8812806670009782 absolute error = 5.963413096665704e-09 relative error = 6.766758151307612e-07 % Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.12 y2[1] (analytic) = 1.992808635853866 y2[1] (numeric) = 1.992807170131894 absolute error = 1.465721972460088e-06 relative error = 7.355056306407788e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 0.8802877927110806 y1[1] (numeric) = 0.8802878000337716 absolute error = 7.32269100911509e-09 relative error = 8.318519318054966e-07 % Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.121 y2[1] (analytic) = 1.992688427262253 y2[1] (numeric) = 1.992686730163909 absolute error = 1.697098343633741e-06 relative error = 8.516626685915859e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 0.8792950440967935 y1[1] (numeric) = 0.8792950529990088 absolute error = 8.902215298256522e-09 relative error = 1.01242641568631e-06 % Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.122 y2[1] (analytic) = 1.992567225982295 y2[1] (numeric) = 1.99256527432023 absolute error = 1.951662064847426e-06 relative error = 9.794711261926415e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 0.8783024161874522 y1[1] (numeric) = 0.8783024269120691 absolute error = 1.072461686124626e-08 relative error = 1.221061978606393e-06 % Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.123 y2[1] (analytic) = 1.992445032135194 y2[1] (numeric) = 1.992442801608229 absolute error = 2.230526965130153e-06 relative error = 0.0001119492346918008 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8773099099756846 y1[1] (numeric) = 0.8773099227893244 absolute error = 1.281363981586736e-08 relative error = 1.460560250165475e-06 % Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.124 y2[1] (analytic) = 1.992321845843143 y2[1] (numeric) = 1.992319311035399 absolute error = 2.534807744147827e-06 relative error = 0.0001272288284865494 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8763175264539969 y1[1] (numeric) = 0.8763175416481395 absolute error = 1.519414261075269e-08 relative error = 1.733862686991497e-06 % Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.125 y2[1] (analytic) = 1.992197667229329 y2[1] (numeric) = 1.992194801609357 absolute error = 2.865619972203248e-06 relative error = 0.0001438421507735546 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8753252666147723 y1[1] (numeric) = 0.8753252845068713 absolute error = 1.789209902458566e-08 relative error = 2.044051475148371e-06 % Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.126 y2[1] (analytic) = 1.992072496417931 y2[1] (numeric) = 1.992069272337843 absolute error = 3.22408008712749e-06 relative error = 0.0001618455198254536 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8743331314502707 y1[1] (numeric) = 0.8743331523848692 absolute error = 2.093459849916712e-08 relative error = 2.394350362137434e-06 % Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.127 y2[1] (analytic) = 1.991946333534119 y2[1] (numeric) = 1.991942722228723 absolute error = 3.611305395168074e-06 relative error = 0.0001812953157608861 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8733411219526273 y1[1] (numeric) = 0.8733411463024747 absolute error = 2.434984747168301e-08 relative error = 2.78812560860999e-06 % Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.128 y2[1] (analytic) = 1.991819178704056 y2[1] (numeric) = 1.991815150289987 absolute error = 4.028414068324437e-06 relative error = 0.0002022479807100491 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8723492391138512 y1[1] (numeric) = 0.8723492672810216 absolute error = 2.816717037390504e-08 relative error = 3.228886908013788e-06 % Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.129 y2[1] (analytic) = 1.991691032054896 y2[1] (numeric) = 1.991686555529752 absolute error = 4.476525144347931e-06 relative error = 0.0002247600191144781 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8713574839258255 y1[1] (numeric) = 0.8713575163428353 absolute error = 3.241700985423535e-08 relative error = 3.720288222944195e-06 % Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.13 y2[1] (analytic) = 1.991561893714788 y2[1] (numeric) = 1.991556936956263 absolute error = 4.95675852518751e-06 relative error = 0.0002488879979492803 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8703658573803051 y1[1] (numeric) = 0.8703658945112333 absolute error = 3.713092810997409e-08 relative error = 4.266128754376194e-06 % Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.131 y2[1] (analytic) = 1.991431763812868 y2[1] (numeric) = 1.991426293577893 absolute error = 5.470234974991328e-06 relative error = 0.0002746885469235368 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8693743604689166 y1[1] (numeric) = 0.8693744028105245 absolute error = 4.234160788652019e-08 relative error = 4.87035387881491e-06 % Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.132 y2[1] (analytic) = 1.991300642479268 y2[1] (numeric) = 1.991294624403147 absolute error = 6.01807612099492e-06 relative error = 0.0003022183588261247 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8683829941831566 y1[1] (numeric) = 0.8683830422660096 absolute error = 4.808285303248283e-08 relative error = 5.537056040314551e-06 % Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.133 y2[1] (analytic) = 1.991168529845107 y2[1] (numeric) = 1.991161928440656 absolute error = 6.601404450856663e-06 relative error = 0.0003315341896936361 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8673917595143915 y1[1] (numeric) = 0.8673918139039808 absolute error = 5.438958927683757e-08 relative error = 6.270475673793296e-06 % Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.134 y2[1] (analytic) = 1.991035426042499 y2[1] (numeric) = 1.991028204699188 absolute error = 7.221343311103467e-06 relative error = 0.0003626928590345095 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8664006574538559 y1[1] (numeric) = 0.8664007187517213 absolute error = 6.129786545017168e-08 relative error = 7.075002185514429e-06 % Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.135 y2[1] (analytic) = 1.990901331204548 y2[1] (numeric) = 1.99089345218764 absolute error = 7.879016908463043e-06 relative error = 0.0003957512501986238 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8654096889926517 y1[1] (numeric) = 0.8654097578375057 absolute error = 6.884485403979568e-08 relative error = 7.955174862894359e-06 % Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.136 y2[1] (analytic) = 1.990766245465348 y2[1] (numeric) = 1.990757669915043 absolute error = 8.575550305423008e-06 relative error = 0.0004307663104574312 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8644188551217472 y1[1] (numeric) = 0.8644189321905997 absolute error = 7.70688525220109e-08 relative error = 8.915683880027849e-06 % Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.137 y2[1] (analytic) = 1.990630168959985 y2[1] (numeric) = 1.990620856890564 absolute error = 9.312069421563152e-06 relative error = 0.0004677950513745248 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8634281568319764 y1[1] (numeric) = 0.8634282428412596 absolute error = 8.600928325108725e-08 relative error = 9.961371142523988e-06 % Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.138 y2[1] (analytic) = 1.990493101824536 y2[1] (numeric) = 1.990483012123504 absolute error = 1.008970103177909e-05 relative error = 0.0005068945490205724 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8624375951140373 y1[1] (numeric) = 0.8624376908207327 absolute error = 9.570669545766464e-08 relative error = 1.109723138229029e-05 % Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.139 y2[1] (analytic) = 1.990355044196067 y2[1] (numeric) = 1.990344134623303 absolute error = 1.090957276472793e-05 relative error = 0.000548121944199883 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8614471709584917 y1[1] (numeric) = 0.861447277161257 absolute error = 1.062027653597752e-07 relative error = 1.232841304030384e-05 % Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.14 y2[1] (analytic) = 1.990215996212637 y2[1] (numeric) = 1.990204223399535 absolute error = 1.177281310216216e-05 relative error = 0.0005915344427220823 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8604568853557635 y1[1] (numeric) = 0.8604570028960608 absolute error = 1.175402972730666e-07 relative error = 1.366021927112228e-05 % Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.141 y2[1] (analytic) = 1.990075958013293 y2[1] (numeric) = 1.990063277461916 absolute error = 1.268055137759738e-05 relative error = 0.0006371893156408194 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8594667392961384 y1[1] (numeric) = 0.8594668690593626 absolute error = 1.297632242769353e-07 relative error = 1.509810890217871e-05 % Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.142 y2[1] (analytic) = 1.989934929738074 y2[1] (numeric) = 1.989921295820299 absolute error = 1.363391777520206e-05 relative error = 0.0006851438995041227 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8584767337697622 y1[1] (numeric) = 0.8584768766863716 absolute error = 1.429166094357726e-07 relative error = 1.664769746387814e-05 % Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.143 y2[1] (analytic) = 1.989792911528007 y2[1] (numeric) = 1.989778277484679 absolute error = 1.46340433284653e-05 relative error = 0.0007354555965940939 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8574868697666405 y1[1] (numeric) = 0.8574870268132867 absolute error = 1.570466462430531e-07 relative error = 1.831475813568928e-05 % Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.144 y2[1] (analytic) = 1.989649903525112 y2[1] (numeric) = 1.989634221465192 absolute error = 1.568205991975269e-05 relative error = 0.0007881818752117344 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8564971482766371 y1[1] (numeric) = 0.8564973204772969 absolute error = 1.722006597315584e-07 relative error = 2.010522277605294e-05 % Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.145 y2[1] (analytic) = 1.989505905872395 y2[1] (numeric) = 1.989489126772116 absolute error = 1.677910027830798e-05 relative error = 0.0008433802698841638 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8555075702894736 y1[1] (numeric) = 0.8555077587165808 absolute error = 1.884271072505328e-07 relative error = 2.202518291997997e-05 % Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.146 y2[1] (analytic) = 1.989360918713855 y2[1] (numeric) = 1.989342992415875 absolute error = 1.792629797980894e-05 relative error = 0.0009011083816504498 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8545181367947277 y1[1] (numeric) = 0.854518342570307 absolute error = 2.057755793538618e-07 relative error = 2.408089079603623e-05 % Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.147 y2[1] (analytic) = 1.989214942194478 y2[1] (numeric) = 1.989195817407033 absolute error = 1.912478744481305e-05 relative error = 0.0009614238782921474 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.8535288487818328 y1[1] (numeric) = 0.8535290730786332 absolute error = 2.24296800466206e-07 relative error = 2.62787603238397e-05 % Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.148 y2[1] (analytic) = 1.989067976460242 y2[1] (numeric) = 1.989047600756304 absolute error = 2.037570393742527e-05 relative error = 0.001024384494575495 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.852539707240077 y1[1] (numeric) = 0.8525399512827069 absolute error = 2.440426298822018e-07 relative error = 2.862536815701405e-05 % Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.149 y2[1] (analytic) = 1.988920021658112 y2[1] (numeric) = 1.988898341474546 absolute error = 2.168018356529799e-05 relative error = 0.001090048032561097 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.8515507131586016 y1[1] (numeric) = 0.8515509782246643 absolute error = 2.650660626546397e-07 relative error = 3.112745471980728e-05 % Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.15 y2[1] (analytic) = 1.988771077936042 y2[1] (numeric) = 1.988748038572765 absolute error = 2.303936327718858e-05 relative error = 0.001158472361791331 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.8505618675264007 y1[1] (numeric) = 0.8505621549476311 absolute error = 2.874212303716206e-07 relative error = 3.379192523731371e-05 % Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1510000000000001 y2[1] (analytic) = 1.988621145442977 y2[1] (numeric) = 1.988596691062115 absolute error = 2.445438086184915e-05 relative error = 0.001229715419545224 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.8495731713323199 y1[1] (numeric) = 0.8495734824957217 absolute error = 3.111634018226894e-07 relative error = 3.662585075923666e-05 % Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1520000000000001 y2[1] (analytic) = 1.988470224328849 y2[1] (numeric) = 1.988444297953901 absolute error = 2.592637494847061e-05 relative error = 0.001303835211172011 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.8485846255650551 y1[1] (numeric) = 0.8485849619140394 absolute error = 3.363489843311029e-07 relative error = 3.963646926871142e-05 % Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1530000000000001 y2[1] (analytic) = 1.988318314744579 y2[1] (numeric) = 1.988290858259576 absolute error = 2.745648500335207e-05 relative error = 0.001380889810235397 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.8475962312131522 y1[1] (numeric) = 0.8475965942486759 absolute error = 3.630355237538296e-07 relative error = 4.28311866410994e-05 % Correct digits = 6 h = 0.001 Finished! Maximum Time Reached before Solution Completed! diff ( y2 , x , 3 ) = m1 * cos(x) ; diff ( y1 , x , 1 ) = m1 * y2 + 1.0; Iterations = 53 Total Elapsed Time = 3 Minutes 3 Seconds Elapsed Time(since restart) = 2 Minutes 59 Seconds Expected Time Remaining = 4 Hours 33 Minutes 42 Seconds Optimized Time Remaining = 4 Hours 27 Minutes 43 Seconds Expected Total Time = 4 Hours 30 Minutes 46 Seconds Time to Timeout Unknown Percent Done = 1.102 %