##############ECHO OF PROBLEM################# ##############temp/div_sin_cpostode.ode################# diff ( y , x , 1 ) = sin(x) / 2.0; ! /* 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 ; array_y_init[0 + 1] = exact_soln_y(x_start); glob_h = 0.05; glob_look_poles = true; glob_max_iter = 1000000; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_h = 0.005 ; glob_display_interval = 0.1; glob_look_poles = true; glob_max_iter = 10000; glob_max_minutes = 10; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(-cos(x)/2.0); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = -0.4975020826390129 y[1] (numeric) = -0.4975020826390129 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.2000000000000001 y[1] (analytic) = -0.4900332889206208 y[1] (numeric) = -0.4900332889206133 absolute error = 7.494005416219807e-15 relative error = 1.529284966073752e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = -0.477668244562803 y[1] (numeric) = -0.4776682445627882 absolute error = 1.482147737874584e-14 relative error = 3.102881036672543e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = -0.4605304970014425 y[1] (numeric) = -0.4605304970014205 absolute error = 2.19824158875781e-14 relative error = 4.773281255141121e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = -0.4387912809451863 y[1] (numeric) = -0.4387912809451574 absolute error = 2.886579864025407e-14 relative error = 6.578480451588549e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = -0.4126678074548391 y[1] (numeric) = -0.4126678074548037 absolute error = 3.530509218307998e-14 relative error = 8.555329867097435e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = -0.382421093642244 y[1] (numeric) = -0.3824210936422028 absolute error = 4.124478536482457e-14 relative error = 1.07851753081929e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = -0.3483533546735825 y[1] (numeric) = -0.3483533546735357 absolute error = 4.679590048795035e-14 relative error = 1.343345768316183e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = -0.310804984135332 y[1] (numeric) = -0.3108049841352802 absolute error = 5.179190409876355e-14 relative error = 1.666379457937267e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = -0.2701511529340696 y[1] (numeric) = -0.2701511529340135 absolute error = 5.612177389480166e-14 relative error = 2.077421224572681e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = -0.2245672166261815 y[1] (numeric) = -0.2245672166261205 absolute error = 6.097899962753672e-14 relative error = 2.715400784836882e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = -0.1788465245009015 y[1] (numeric) = -0.1788465245008364 absolute error = 6.50868248186498e-14 relative error = 3.639255780915201e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = -0.1313388570216096 y[1] (numeric) = -0.1313388570215412 absolute error = 6.838973831690964e-14 relative error = 5.207121477055131e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = -0.08251889509781175 y[1] (numeric) = -0.0825188950977407 absolute error = 7.105427357601002e-14 relative error = 8.610667107428858e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = -0.03287443165131678 y[1] (numeric) = -0.03287443165124375 absolute error = 7.303185833862358e-14 relative error = 2.221539800694875e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 0.01709850224939582 y[1] (numeric) = 0.01709850224947005 absolute error = 7.423228698399953e-14 relative error = 4.341449672097599e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 0.06690059356764584 y[1] (numeric) = 0.0669005935677205 absolute error = 7.466249840604178e-14 relative error = 1.116021464451546e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 0.116034236269364 y[1] (numeric) = 0.1160342362694383 absolute error = 7.43016759230386e-14 relative error = 6.403426980857038e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 0.1640085032380978 y[1] (numeric) = 0.164008503238171 absolute error = 7.321920847402907e-14 relative error = 4.464354410193829e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 0.2103440514564799 y[1] (numeric) = 0.2103440514565512 absolute error = 7.130407375655068e-14 relative error = 3.389878309503964e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 0.2545779114432079 y[1] (numeric) = 0.2545779114432766 absolute error = 6.872280522429719e-14 relative error = 2.699480282272176e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 0.2962681130910648 y[1] (numeric) = 0.2962681130911301 absolute error = 6.533662499919046e-14 relative error = 2.205320860132787e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 0.3349981016861334 y[1] (numeric) = 0.3349981016861949 absolute error = 6.150635556423367e-14 relative error = 1.836021017870132e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 0.3703808999848042 y[1] (numeric) = 0.3703808999848611 absolute error = 5.689893001203927e-14 relative error = 1.5362274354421e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 0.4020629747624748 y[1] (numeric) = 0.4020629747625266 absolute error = 5.179190409876355e-14 relative error = 1.288154029337331e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 0.4297277692006684 y[1] (numeric) = 0.4297277692007145 absolute error = 4.612976667317525e-14 relative error = 1.073464876588746e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 0.4530988658181236 y[1] (numeric) = 0.4530988658181636 absolute error = 3.996802888650564e-14 relative error = 8.821039270168691e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 0.4719427483428964 y[1] (numeric) = 0.4719427483429299 absolute error = 3.347322419244847e-14 relative error = 7.092645095190242e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 0.4860711349297587 y[1] (numeric) = 0.486071134929785 absolute error = 2.636779683484747e-14 relative error = 5.424678599493022e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 0.495342859410158 y[1] (numeric) = 0.4953428594101772 absolute error = 1.915134717478395e-14 relative error = 3.866281063905695e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 0.4996652817779111 y[1] (numeric) = 0.4996652817779229 absolute error = 1.17128529097954e-14 relative error = 2.344139834594607e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 0.4989952138175222 y[1] (numeric) = 0.4989952138175263 absolute error = 4.107825191113079e-15 relative error = 8.232193570929263e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 0.4933393506265564 y[1] (numeric) = 0.4933393506265529 absolute error = 3.441691376337985e-15 relative error = 6.976316346885627e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 0.482754203720438 y[1] (numeric) = 0.4827542037204269 absolute error = 1.110223024625157e-14 relative error = 2.299768735453797e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 0.4673455363880687 y[1] (numeric) = 0.46734553638805 absolute error = 1.865174681370263e-14 relative error = 3.990997102027485e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 0.4472673069400052 y[1] (numeric) = 0.4472673069399791 absolute error = 2.609024107869118e-14 relative error = 5.833254672063663e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 0.4227201304079123 y[1] (numeric) = 0.4227201304078789 absolute error = 3.341771304121721e-14 relative error = 7.905399018724306e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 0.393949274065481 y[1] (numeric) = 0.3939492740654408 absolute error = 4.024558464266192e-14 relative error = 1.021593065201903e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 0.3612422067989041 y[1] (numeric) = 0.3612422067988574 absolute error = 4.668487818548783e-14 relative error = 1.292342846623023e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 0.3249257268127902 y[1] (numeric) = 0.3249257268127375 absolute error = 5.268008251846368e-14 relative error = 1.621296135433927e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 0.2853626963705284 y[1] (numeric) = 0.2853626963704701 absolute error = 5.823119764158946e-14 relative error = 2.040603007408485e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 0.2429484161944984 y[1] (numeric) = 0.2429484161944353 absolute error = 6.317169010117141e-14 relative error = 2.600209998924122e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 0.1981066757519224 y[1] (numeric) = 0.1981066757518549 absolute error = 6.747380432159389e-14 relative error = 3.405932892745495e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 0.1512855188905938 y[1] (numeric) = 0.1512855188905227 absolute error = 7.113754030285691e-14 relative error = 4.702204204640494e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 0.1029527671328542 y[1] (numeric) = 0.1029527671327801 absolute error = 7.413514246934483e-14 relative error = 7.200888770058799e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 0.05359134535758335 y[1] (numeric) = 0.05359134535750695 absolute error = 7.639722188201858e-14 relative error = 1.425551483588723e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 0.003694456574443073 y[1] (numeric) = 0.003694456574365168 absolute error = 7.790513026351142e-14 relative error = 2.108703369324495e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = -0.04623934599756405 y[1] (numeric) = -0.04623934599764271 absolute error = 7.865236240078843e-14 relative error = 1.700983452597533e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = -0.09571114030905918 y[1] (numeric) = -0.09571114030913781 absolute error = 7.863154571907671e-14 relative error = 8.215506101501763e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = -0.1442266205444828 y[1] (numeric) = -0.1442266205445607 absolute error = 7.788214517745473e-14 relative error = 5.39998405865955e-11 % Correct digits = 12 h = 0.005 Finished! diff ( y , x , 1 ) = sin(x) / 2.0; Iterations = 981 Total Elapsed Time = 1 Minutes 2 Seconds Elapsed Time(since restart) = 1 Minutes 2 Seconds Time to Timeout = 8 Minutes 58 Seconds Percent Done = 100.2 %