##############ECHO OF PROBLEM################# ##############temp/lin_arctanpostode.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=c(-1.0); x_end=c(-0.6); 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=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(c(10.0) * (c(0.1) * c(x) + c(0.2)) * arctan(c(0.1) * c(x) + c(0.2))-c(5.0) * ln(c(1.0) + expt((c(0.1) * c(x) + c(0.2)) , c(2)))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -1 y[1] (closed_form) = 0.04991699822532158 y[1] (numeric) = 0.04991699822532158 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.99 y[1] (closed_form) = 0.0509186349177335 y[1] (numeric) = 0.05091863492429724 absolute error = 6.56373566609858e-12 relative error = 1.289063557321058e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.98 y[1] (closed_form) = 0.05193017062867282 y[1] (numeric) = 0.0519301706418644 absolute error = 1.319157977297536e-11 relative error = 2.540253500667632e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.97 y[1] (closed_form) = 0.0529516033693342 y[1] (numeric) = 0.05295160338921538 absolute error = 1.988118697449082e-11 relative error = 3.754595840246943e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.96 y[1] (closed_form) = 0.05398293113212667 y[1] (numeric) = 0.0539829311587592 absolute error = 2.663252951506934e-11 relative error = 4.933509343885852e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.95 y[1] (closed_form) = 0.05502415189069715 y[1] (numeric) = 0.05502415192414486 absolute error = 3.34477098795638e-11 relative error = 6.078732471153046e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9399999999999999 y[1] (closed_form) = 0.05607526359996047 y[1] (numeric) = 0.05607526364028493 absolute error = 4.032445904966764e-11 relative error = 7.191131429598141e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9299999999999999 y[1] (closed_form) = 0.0571362641961155 y[1] (numeric) = 0.05713626424337928 absolute error = 4.7263776226103e-11 relative error = 8.272115247835245e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9199999999999999 y[1] (closed_form) = 0.05820715159667454 y[1] (numeric) = 0.05820715165093907 absolute error = 5.426452343026966e-11 relative error = 9.322655711840377e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9099999999999999 y[1] (closed_form) = 0.05928792370048203 y[1] (numeric) = 0.05928792376181079 absolute error = 6.132876845255097e-11 relative error = 1.034422604548932e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8999999999999999 y[1] (closed_form) = 0.06037857838774653 y[1] (numeric) = 0.0603785784562008 absolute error = 6.845427003021598e-11 relative error = 1.133750940451231e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8899999999999999 y[1] (closed_form) = 0.06147911352005771 y[1] (numeric) = 0.06147911359569971 absolute error = 7.564200654730513e-11 relative error = 1.230369180951621e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8799999999999999 y[1] (closed_form) = 0.06258952694041534 y[1] (numeric) = 0.06258952702330728 absolute error = 8.28919433093489e-11 relative error = 1.32437401848813e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8699999999999999 y[1] (closed_form) = 0.06370981647325438 y[1] (numeric) = 0.06370981656345723 absolute error = 9.020284519323241e-11 relative error = 1.41583903684764e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8599999999999999 y[1] (closed_form) = 0.06483997992446676 y[1] (numeric) = 0.06483998002204251 absolute error = 9.757575303304122e-11 relative error = 1.504870191920308e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8499999999999999 y[1] (closed_form) = 0.06598001508143005 y[1] (numeric) = 0.06598001518644066 absolute error = 1.050106113176241e-10 relative error = 1.591551793191074e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8399999999999999 y[1] (closed_form) = 0.06712991971303305 y[1] (numeric) = 0.06712991982553923 absolute error = 1.125061849238662e-10 relative error = 1.675946960830694e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8299999999999998 y[1] (closed_form) = 0.068289691569697 y[1] (numeric) = 0.06828969168976161 absolute error = 1.200646110310899e-10 relative error = 1.758165958452909e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8199999999999998 y[1] (closed_form) = 0.06945932838340939 y[1] (numeric) = 0.06945932851109299 absolute error = 1.276835998043069e-10 relative error = 1.838249847443163e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8099999999999998 y[1] (closed_form) = 0.0706388278677423 y[1] (numeric) = 0.07063882800310646 absolute error = 1.353641643220271e-10 relative error = 1.916285538818264e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7999999999999998 y[1] (closed_form) = 0.07182818771788424 y[1] (numeric) = 0.0718281878609893 absolute error = 1.43105055583348e-10 relative error = 1.992324463836037e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7899999999999998 y[1] (closed_form) = 0.07302740561066216 y[1] (numeric) = 0.07302740576156959 absolute error = 1.509074254446574e-10 relative error = 2.066449221121236e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7799999999999998 y[1] (closed_form) = 0.07423647920457176 y[1] (numeric) = 0.07423647936334281 absolute error = 1.587710518613505e-10 relative error = 2.138720122001325e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7699999999999998 y[1] (closed_form) = 0.07545540613980296 y[1] (numeric) = 0.07545540630649884 absolute error = 1.666958793222761e-10 relative error = 2.209197297453065e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7599999999999998 y[1] (closed_form) = 0.07668418403826716 y[1] (numeric) = 0.07668418421294901 absolute error = 1.74681852316283e-10 relative error = 2.277938462892332e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7499999999999998 y[1] (closed_form) = 0.07792281050362559 y[1] (numeric) = 0.07792281068635337 absolute error = 1.827277773536196e-10 relative error = 2.344984429753308e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7399999999999998 y[1] (closed_form) = 0.07917128312131357 y[1] (numeric) = 0.07917128331214819 absolute error = 1.908346258794325e-10 relative error = 2.410402084642458e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7299999999999998 y[1] (closed_form) = 0.08042959945857128 y[1] (numeric) = 0.08042959965757361 absolute error = 1.990023285047826e-10 relative error = 2.474242441146152e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7199999999999998 y[1] (closed_form) = 0.08169775706447183 y[1] (numeric) = 0.0816977572717015 absolute error = 2.072296778621308e-10 relative error = 2.536540601703366e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7099999999999997 y[1] (closed_form) = 0.08297575346994582 y[1] (numeric) = 0.0829757536854635 absolute error = 2.155176870299869e-10 relative error = 2.597357396797226e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6999999999999997 y[1] (closed_form) = 0.08426358618781293 y[1] (numeric) = 0.08426358641167916 absolute error = 2.238662311082606e-10 relative error = 2.656737521345116e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6899999999999997 y[1] (closed_form) = 0.08556125271280927 y[1] (numeric) = 0.08556125294508456 absolute error = 2.322752823413765e-10 relative error = 2.714725123544186e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6799999999999997 y[1] (closed_form) = 0.08686875052161584 y[1] (numeric) = 0.08686875076236059 absolute error = 2.407447435848198e-10 relative error = 2.771361877996789e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6699999999999997 y[1] (closed_form) = 0.08818607707288864 y[1] (numeric) = 0.08818607732216198 absolute error = 2.492733380821122e-10 relative error = 2.826674531355779e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6599999999999997 y[1] (closed_form) = 0.08951322980728404 y[1] (numeric) = 0.08951323006514617 absolute error = 2.57862120545127e-10 relative error = 2.88071518702081e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6499999999999997 y[1] (closed_form) = 0.09085020614749255 y[1] (numeric) = 0.0908502064140024 absolute error = 2.665098558507495e-10 relative error = 2.933508542821343e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6399999999999997 y[1] (closed_form) = 0.09219700349826254 y[1] (numeric) = 0.09219700377348124 absolute error = 2.752186950560898e-10 relative error = 2.985115400863069e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6299999999999997 y[1] (closed_form) = 0.09355361924643742 y[1] (numeric) = 0.09355361953042374 absolute error = 2.839863205705839e-10 relative error = 3.035546062868095e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6199999999999997 y[1] (closed_form) = 0.09492005076097768 y[1] (numeric) = 0.09492005105379142 absolute error = 2.92813745472742e-10 relative error = 3.084846069141798e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6099999999999997 y[1] (closed_form) = 0.09629629539299625 y[1] (numeric) = 0.09629629569469601 absolute error = 3.016997623950246e-10 relative error = 3.133036023491384e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 Finished! diff ( y , x , 1 ) = arctan ( 0.1 * x + 0.2 ) ; Iterations = 400 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.3 %