##############ECHO OF PROBLEM################# ##############temp/lin_arctan_sm_hpostode.ode################# diff ( y , x , 1 ) = arctan ( 0.1 * x + 0.2 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-1.0; x_end=-0.6; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.000001; glob_type_given_pole=0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(10.0 * (0.1 * x + 0.2) * arctan(0.1 * x + 0.2) - 5.0 * ln(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 = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 400000.0000000001 step_error = 5.270462766947299e-15 est_needed_step_err = 5.270462766947299e-15 opt_iter = 1 SETTING H FOR MAX H 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] = -1 y[1] (analytic) = 0.04991699822532158 y[1] (numeric) = 0.04991699822532158 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 1e-06 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] = -0.9899999999997124 y[1] (analytic) = 0.05091863491776152 y[1] (numeric) = 0.05091863491773294 absolute error = 2.858824288409778e-14 relative error = 5.61449515099345e-11 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 13 h = 1e-06 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] = -0.9799999999994249 y[1] (analytic) = 0.0519301706287322 y[1] (numeric) = 0.05193017062867358 absolute error = 5.861977570020827e-14 relative error = 1.128819239191461e-10 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 12 h = 1e-06 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] = -0.9699999999991373 y[1] (analytic) = 0.05295160336942276 y[1] (numeric) = 0.05295160336933587 absolute error = 8.688882946472631e-14 relative error = 1.64091026401102e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.9599999999988498 y[1] (analytic) = 0.05398293113224559 y[1] (numeric) = 0.05398293113212851 absolute error = 1.170730179467228e-13 relative error = 2.168704356936847e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.9499999999985622 y[1] (analytic) = 0.05502415189084753 y[1] (numeric) = 0.05502415189070092 absolute error = 1.466188281895597e-13 relative error = 2.664626771175143e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.9399999999982747 y[1] (analytic) = 0.05607526360014237 y[1] (numeric) = 0.0560752635999659 absolute error = 1.764630108702647e-13 relative error = 3.146895788641762e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.9299999999979871 y[1] (analytic) = 0.05713626419633006 y[1] (numeric) = 0.05713626419612296 absolute error = 2.07105166349919e-13 relative error = 3.624758623319683e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.9199999999976995 y[1] (analytic) = 0.05820715159692179 y[1] (numeric) = 0.05820715159668305 absolute error = 2.387395836578321e-13 relative error = 4.101550704818505e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.909999999997412 y[1] (analytic) = 0.05928792370076309 y[1] (numeric) = 0.05928792370049342 absolute error = 2.696731726814505e-13 relative error = 4.548534606179497e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.8999999999971244 y[1] (analytic) = 0.06037857838806147 y[1] (numeric) = 0.06037857838776042 absolute error = 3.010439120210151e-13 relative error = 4.985939054181837e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.8899999999968369 y[1] (analytic) = 0.06147911352040762 y[1] (numeric) = 0.06147911352007464 absolute error = 3.329767017667962e-13 relative error = 5.416094714122164e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.8799999999965493 y[1] (analytic) = 0.06258952694080031 y[1] (numeric) = 0.06258952694043589 absolute error = 3.644168300453998e-13 relative error = 5.822329195586986e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.8699999999962618 y[1] (analytic) = 0.0637098164736755 y[1] (numeric) = 0.06370981647327792 absolute error = 3.975847429060764e-13 relative error = 6.2405570273516e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.8599999999959742 y[1] (analytic) = 0.06483997992492409 y[1] (numeric) = 0.06483997992449338 absolute error = 4.307110224033295e-13 relative error = 6.642676677291302e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.8499999999956867 y[1] (analytic) = 0.06598001508192364 y[1] (numeric) = 0.06598001508146116 absolute error = 4.624772786954168e-13 relative error = 7.00935394029821e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.8399999999953991 y[1] (analytic) = 0.06712991971356401 y[1] (numeric) = 0.0671299197130676 absolute error = 4.964084698855231e-13 relative error = 7.394742493416401e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.8299999999951115 y[1] (analytic) = 0.06828969157026649 y[1] (numeric) = 0.06828969156973744 absolute error = 5.290490268095027e-13 relative error = 7.747128660921528e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.819999999994824 y[1] (analytic) = 0.06945932838401746 y[1] (numeric) = 0.06945932838345437 absolute error = 5.630912403020716e-13 relative error = 8.106776345272559e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.8099999999945364 y[1] (analytic) = 0.07063882786839008 y[1] (numeric) = 0.07063882786779312 absolute error = 5.969669203409467e-13 relative error = 8.450974320428685e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.7999999999942489 y[1] (analytic) = 0.07182818771857061 y[1] (numeric) = 0.07182818771793974 absolute error = 6.308703559554374e-13 relative error = 8.78304710160926e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.7899999999939613 y[1] (analytic) = 0.07302740561138833 y[1] (numeric) = 0.07302740561072357 absolute error = 6.647599137821203e-13 relative error = 9.102882790600651e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.7799999999936738 y[1] (analytic) = 0.07423647920533881 y[1] (numeric) = 0.07423647920463913 absolute error = 6.996764279065815e-13 relative error = 9.424967824393582e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.7699999999933862 y[1] (analytic) = 0.07545540614061204 y[1] (numeric) = 0.07545540613987629 absolute error = 7.357447984190912e-13 relative error = 9.750723454433763e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = -0.7599999999930986 y[1] (analytic) = 0.07668418403911831 y[1] (numeric) = 0.07668418403834702 absolute error = 7.712858129949041e-13 relative error = 1.005795161882995e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 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] = -0.7499999999928111 y[1] (analytic) = 0.07792281050451995 y[1] (numeric) = 0.07792281050371229 absolute error = 8.076594948391858e-13 relative error = 1.036486607207702e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 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] = -0.7399999999925235 y[1] (analytic) = 0.07917128312225005 y[1] (numeric) = 0.07917128312140795 absolute error = 8.421041641781812e-13 relative error = 1.063648498506549e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 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] = -0.729999999992236 y[1] (analytic) = 0.08042959945955215 y[1] (numeric) = 0.08042959945867369 absolute error = 8.784639682346551e-13 relative error = 1.092214774333711e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 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] = -0.7199999999919484 y[1] (analytic) = 0.08169775706549712 y[1] (numeric) = 0.08169775706458045 absolute error = 9.166695180695683e-13 relative error = 1.122025317457215e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 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] = -0.7099999999916609 y[1] (analytic) = 0.08297575347101553 y[1] (numeric) = 0.08297575347006245 absolute error = 9.530848332772734e-13 relative error = 1.148630525675429e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 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] = -0.6999999999913733 y[1] (analytic) = 0.08426358618892715 y[1] (numeric) = 0.08426358618793754 absolute error = 9.896111707874411e-13 relative error = 1.174423277652385e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 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] = -0.6899999999910857 y[1] (analytic) = 0.08556125271397017 y[1] (numeric) = 0.08556125271294271 absolute error = 1.027455898139351e-12 relative error = 1.200842514045603e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 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] = -0.6799999999907982 y[1] (analytic) = 0.08686875052282353 y[1] (numeric) = 0.08686875052175853 absolute error = 1.064995314159489e-12 relative error = 1.225982079573801e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 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] = -0.6699999999905106 y[1] (analytic) = 0.08818607707414304 y[1] (numeric) = 0.08818607707304034 absolute error = 1.102701263633321e-12 relative error = 1.250425577618355e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 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] = -0.6599999999902231 y[1] (analytic) = 0.08951322980858638 y[1] (numeric) = 0.08951322980744494 absolute error = 1.141434169404931e-12 relative error = 1.275156948135773e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 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] = -0.6499999999899355 y[1] (analytic) = 0.09085020614884282 y[1] (numeric) = 0.09085020614766255 absolute error = 1.180264219691196e-12 relative error = 1.299132131585405e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 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] = -0.639999999989648 y[1] (analytic) = 0.09219700349966184 y[1] (numeric) = 0.09219700349844352 absolute error = 1.218317113860223e-12 relative error = 1.321428102448787e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 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] = -0.6299999999893604 y[1] (analytic) = 0.09355361924788583 y[1] (numeric) = 0.09355361924662839 absolute error = 1.257438597690452e-12 relative error = 1.344083326545241e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 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] = -0.6199999999890728 y[1] (analytic) = 0.09492005076247631 y[1] (numeric) = 0.09492005076117863 absolute error = 1.297684182333114e-12 relative error = 1.367133889951641e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 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] = -0.6099999999887853 y[1] (analytic) = 0.09629629539454515 y[1] (numeric) = 0.09629629539320725 absolute error = 1.337902011400161e-12 relative error = 1.389359794079833e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 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 ) = arctan ( 0.1 * x + 0.2 ) ; Iterations = 400000 Total Elapsed Time = 18.0 Seconds Elapsed Time(since restart) = 18.0 Seconds Time to Timeout = 9 Minutes 42.0 Seconds Percent Done = 100 %