##############ECHO OF PROBLEM################# ##############temp/diff2postode.ode################# diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ; ! /* 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); array_y_init[1 + 1] = exact_soln_yp(x_start); array_y_init[2 + 1] = exact_soln_ypp(x_start); glob_h = 0.001 ; glob_look_poles = true; /* 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(2.0 - cos(x)); } double exact_soln_yp (double x) { return( sin(x)); } double exact_soln_ypp (double x) { return( cos(x)); } double exact_soln_yppp (double x) { return( -sin(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 1.004995834721974 y[1] (numeric) = 1.004995834721974 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) = 1.019933422158758 y[1] (numeric) = 1.019954197213047 absolute error = 2.07750542888796e-05 relative error = 0.002036902981854226 % Correct digits = 4 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 1.044663510874394 y[1] (numeric) = 1.0448626013569 absolute error = 0.0001990904825064366 relative error = 0.01905785742815845 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 1.078939005997115 y[1] (numeric) = 1.079721047153534 absolute error = 0.0007820411564187779 relative error = 0.07248242505571895 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 1.122417438109627 y[1] (numeric) = 1.124529534602948 absolute error = 0.002112096493320115 relative error = 0.1881738844753964 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 1.174664385090322 y[1] (numeric) = 1.179288063705141 absolute error = 0.004623678614819271 relative error = 0.3936169916706675 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 1.235157812715512 y[1] (numeric) = 1.243996634460115 absolute error = 0.008838821744603376 relative error = 0.7156026261268673 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 1.303293290652835 y[1] (numeric) = 1.31865524686787 absolute error = 0.01536195621503489 relative error = 1.17870293089132 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 1.378390031729336 y[1] (numeric) = 1.403263900928405 absolute error = 0.02487386919906864 relative error = 1.804559567792415 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 1.459697694131861 y[1] (numeric) = 1.49782259664172 absolute error = 0.03812490250985867 relative error = 2.611835496015703 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 1.550865566747637 y[1] (numeric) = 1.607817959469505 absolute error = 0.05695239272186803 relative error = 3.672297196029986 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 1.642306950998197 y[1] (numeric) = 1.722774240571019 absolute error = 0.08046728957282245 relative error = 4.899649820267417 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 1.737322285956781 y[1] (numeric) = 1.847680563325314 absolute error = 0.110358277368533 relative error = 6.352205244852213 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 1.834962209804377 y[1] (numeric) = 1.982536927732389 absolute error = 0.1475747179280122 relative error = 8.042384586423992 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 1.934251136697366 y[1] (numeric) = 2.127343333792244 absolute error = 0.1930921970948773 relative error = 9.982788347979067 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 2.034197004498792 y[1] (numeric) = 2.282099781504879 absolute error = 0.2479027770060873 relative error = 12.18676344807461 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 2.133801187135292 y[1] (numeric) = 2.446806270870294 absolute error = 0.3130050837350025 relative error = 14.66889631621321 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 2.232068472538728 y[1] (numeric) = 2.62146280188849 absolute error = 0.3893943293497619 relative error = 17.44544731223543 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 2.328017006476196 y[1] (numeric) = 2.806069374559466 absolute error = 0.47805236808327 relative error = 20.53474552605929 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 2.42068810291296 y[1] (numeric) = 3.000625988883222 absolute error = 0.5799378859702622 relative error = 23.95756335863295 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 2.509155822886416 y[1] (numeric) = 3.205132644859758 absolute error = 0.6959768219733422 relative error = 27.73748906405992 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 2.592536226182129 y[1] (numeric) = 3.419589342489075 absolute error = 0.8270531163069457 relative error = 31.90131377739306 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 2.669996203372267 y[1] (numeric) = 3.643996081771173 absolute error = 0.9739998783989066 relative error = 36.47944806695688 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 2.740761799969608 y[1] (numeric) = 3.878352862706052 absolute error = 1.137591062736443 relative error = 41.50638201207627 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 2.80412594952495 y[1] (numeric) = 4.122659685293711 absolute error = 1.318533735768761 relative error = 47.02120231055013 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 2.859455538401337 y[1] (numeric) = 4.376916549534151 absolute error = 1.517461011132814 relative error = 53.0681799648193 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 2.906197731636247 y[1] (numeric) = 4.641123455427372 absolute error = 1.734925723791124 relative error = 59.69744263802472 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 2.943885496685793 y[1] (numeric) = 4.915280402973373 absolute error = 1.97139490628758 relative error = 66.96574674887877 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 2.972142269859517 y[1] (numeric) = 5.199387392172156 absolute error = 2.227245122312639 relative error = 74.93736571425677 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 2.990685718820316 y[1] (numeric) = 5.493444423023718 absolute error = 2.502758704203401 relative error = 83.68511236247923 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 2.999330563555823 y[1] (numeric) = 5.797451495528061 absolute error = 2.798120931972238 relative error = 93.29151531250218 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 2.997990427635044 y[1] (numeric) = 6.111408609685185 absolute error = 3.113418182050141 relative error = 103.8501708795032 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 2.986678701253113 y[1] (numeric) = 6.43531576549509 absolute error = 3.448637064241977 relative error = 115.4672935791534 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 2.965508407440876 y[1] (numeric) = 6.769172962957776 absolute error = 3.8036645555169 relative error = 128.2634891869797 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 2.934691072776137 y[1] (numeric) = 7.112980202073244 absolute error = 4.178289129297106 relative error = 142.3757739973822 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 2.894534613880011 y[1] (numeric) = 7.466737482841492 absolute error = 4.572202868961481 relative error = 157.95986156243 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 2.845440260815825 y[1] (numeric) = 7.830444805262522 absolute error = 4.985004544446697 relative error = 175.1927324953725 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 2.787898548130962 y[1] (numeric) = 8.204102169336331 absolute error = 5.416203621205368 relative error = 194.2754920130236 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 2.722484413597808 y[1] (numeric) = 8.587709575062924 absolute error = 5.865225161465116 relative error = 215.4365010198212 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 2.64985145362558 y[1] (numeric) = 8.981267022442296 absolute error = 6.331415568816716 relative error = 238.9347357624121 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 2.570725392741056 y[1] (numeric) = 9.384774511474449 absolute error = 6.814049118733392 relative error = 265.0632828373729 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 2.485896832388997 y[1] (numeric) = 9.798232042159384 absolute error = 7.312335209770387 relative error = 294.1528029038553 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 2.396213351503845 y[1] (numeric) = 10.2216396144971 absolute error = 7.825426262993253 relative error = 326.5746874368293 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 2.302571037781187 y[1] (numeric) = 10.65499722848759 absolute error = 8.352426190706407 relative error = 362.743474735746 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 2.205905534265709 y[1] (numeric) = 11.09830488413087 absolute error = 8.892399349865162 relative error = 403.1178675484498 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 2.107182690715167 y[1] (numeric) = 11.55156258142693 absolute error = 9.444379890711762 relative error = 448.1993864284444 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 2.007388913148886 y[1] (numeric) = 12.01477032037577 absolute error = 10.00738140722688 relative error = 498.5272829632612 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 1.907521308004872 y[1] (numeric) = 12.48792810097738 absolute error = 10.58040679297251 relative error = 554.667816740608 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 1.808577719381882 y[1] (numeric) = 12.97103592323178 absolute error = 11.1624582038499 relative error = 617.1953842085868 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 1.711546758911034 y[1] (numeric) = 13.46409378713896 absolute error = 11.75254702822793 relative error = 686.6623401925314 % Correct digits = 0 h = 0.005 Finished! diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ; Iterations = 981 Total Elapsed Time = 1 Minutes 38 Seconds Elapsed Time(since restart) = 1 Minutes 38 Seconds Time to Timeout = 8 Minutes 22 Seconds Percent Done = 100.2 %