##############ECHO OF PROBLEM################# ##############temp/h2sinpostode.ode################# diff ( y , x , 2 ) = sin(x); ! /* 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); glob_h = 0.00001; glob_look_poles = true; glob_max_iter = 100; /* 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)); } /* 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) = 1.015643678766263 absolute error = 0.004289743392495327 relative error = 0.420590530646186 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 1.044663510874394 y[1] (numeric) = 1.028276561092581 absolute error = 0.01638694978181277 relative error = 1.568634264644385 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 1.078939005997115 y[1] (numeric) = 1.04386218363794 absolute error = 0.03507682235917464 relative error = 3.251047757491903 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 1.122417438109627 y[1] (numeric) = 1.063338745535129 absolute error = 0.0590786925744986 relative error = 5.263522337464641 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 1.174664385090322 y[1] (numeric) = 1.087605568937104 absolute error = 0.0870588161532182 relative error = 7.411377858921303 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 1.235157812715512 y[1] (numeric) = 1.117514113287319 absolute error = 0.1176436994281929 relative error = 9.524588535739538 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 1.303293290652835 y[1] (numeric) = 1.153859467818417 absolute error = 0.1494338228344179 relative error = 11.46586297237552 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 1.378390031729336 y[1] (numeric) = 1.19737240728344 absolute error = 0.1810176244458965 relative error = 13.13254015764977 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 1.459697694131861 y[1] (numeric) = 1.248712090296057 absolute error = 0.210985603835804 relative error = 14.45406159672571 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 1.550865566747637 y[1] (numeric) = 1.311676830056817 absolute error = 0.2391887366908201 relative error = 15.42291877641138 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 1.642306950998197 y[1] (numeric) = 1.380785562673593 absolute error = 0.2615213883246044 relative error = 15.92402614904913 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 1.737322285956781 y[1] (numeric) = 1.45922490805772 absolute error = 0.2780973778990614 relative error = 16.00724172751328 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 1.834962209804377 y[1] (numeric) = 1.54730505172006 absolute error = 0.2876571580843164 relative error = 15.67646224796004 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 1.934251136697366 y[1] (numeric) = 1.645239851501904 absolute error = 0.2890112851954625 relative error = 14.94176633593372 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 2.034197004498792 y[1] (numeric) = 1.753144700778112 absolute error = 0.2810523037206798 relative error = 13.8163758524425 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 2.133801187135292 y[1] (numeric) = 1.871035375484656 absolute error = 0.2627658116506353 relative error = 12.31444678327357 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 2.232068472538728 y[1] (numeric) = 1.998827876490685 absolute error = 0.233240596048043 relative error = 10.44952692615016 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 2.328017006476196 y[1] (numeric) = 2.136339268890069 absolute error = 0.1916777375861263 relative error = 8.233519645814761 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 2.42068810291296 y[1] (numeric) = 2.283289509826518 absolute error = 0.1373985930864414 relative error = 5.676013895433345 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 2.509155822886416 y[1] (numeric) = 2.439304246589226 absolute error = 0.06985157629718985 relative error = 2.783867612368365 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 2.592536226182129 y[1] (numeric) = 2.603918557021415 absolute error = 0.01138233083928553 relative error = 0.439042306307426 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 2.669996203372267 y[1] (numeric) = 2.776581594868843 absolute error = 0.106585391496576 relative error = 3.991967904746687 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 2.740761799969608 y[1] (numeric) = 2.95666209365349 absolute error = 0.2159002936838816 relative error = 7.877382619907929 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 2.80412594952495 y[1] (numeric) = 3.143454674079539 absolute error = 0.3393287245545893 relative error = 12.10105147424192 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 2.859455538401337 y[1] (numeric) = 3.336186891950129 absolute error = 0.476731353548792 relative error = 16.67210233369541 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 2.906197731636247 y[1] (numeric) = 3.534026956174439 absolute error = 0.6278292245381913 relative error = 21.60311453359751 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 2.943885496685793 y[1] (numeric) = 3.736092039749308 absolute error = 0.7922065430635157 relative error = 26.91023628314948 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 2.972142269859517 y[1] (numeric) = 3.941457100674835 absolute error = 0.9693148308153177 relative error = 32.61333889178642 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 2.990685718820316 y[1] (numeric) = 4.149164124668255 absolute error = 1.158478405847939 relative error = 38.73621352312819 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 2.999330563555823 y[1] (numeric) = 4.358231697325977 absolute error = 1.358901133770155 relative error = 45.30681446993042 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 2.997990427635044 y[1] (numeric) = 4.567664810091897 absolute error = 1.569674382456853 relative error = 52.35755151143314 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 2.986678701253113 y[1] (numeric) = 4.776464802053981 absolute error = 1.789786100800868 relative error = 59.9256324441572 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 2.965508407440876 y[1] (numeric) = 4.983639338233985 absolute error = 2.018130930793109 relative error = 68.05345504094124 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 2.934691072776137 y[1] (numeric) = 5.188212324670535 absolute error = 2.253521251894397 relative error = 76.78904511617394 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 2.894534613880011 y[1] (numeric) = 5.389233661227336 absolute error = 2.494699047347325 relative error = 86.18653359281404 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 2.845440260815825 y[1] (numeric) = 5.585788734679667 absolute error = 2.740348473863842 relative error = 96.30665987266759 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 2.787898548130962 y[1] (numeric) = 5.777007557227408 absolute error = 2.989109009096445 relative error = 107.2172805965402 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 2.722484413597808 y[1] (numeric) = 5.962073459125535 absolute error = 3.239589045527727 relative error = 118.9938509600706 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 2.64985145362558 y[1] (numeric) = 6.140231248578276 absolute error = 3.490379794952696 relative error = 131.7198286785883 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 2.570725392741056 y[1] (numeric) = 6.310794757365898 absolute error = 3.740069364624841 relative error = 145.4869265766641 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 2.485896832388997 y[1] (numeric) = 6.473153696810733 absolute error = 3.987256864421737 relative error = 160.395106203579 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 2.396213351503845 y[1] (numeric) = 6.626779755579919 absolute error = 4.230566404076074 relative error = 176.5521589060926 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 2.302571037781187 y[1] (numeric) = 6.771231878397595 absolute error = 4.468660840616407 relative error = 194.0726590968727 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 2.205905534265709 y[1] (numeric) = 6.906160672923431 absolute error = 4.700255138657723 relative error = 213.0759937651782 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 2.107182690715167 y[1] (numeric) = 7.031311900765397 absolute error = 4.92412921005023 relative error = 233.6830703738842 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 2.007388913148886 y[1] (numeric) = 7.146529017745727 absolute error = 5.139140104596841 relative error = 256.0111830315602 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 1.907521308004872 y[1] (numeric) = 7.251754738038611 absolute error = 5.344233430033739 relative error = 280.1663817650046 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 1.808577719381882 y[1] (numeric) = 7.347031606551221 absolute error = 5.538453887169339 relative error = 306.2325620743696 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 1.711546758911034 y[1] (numeric) = 7.432501573829064 absolute error = 5.720954814918029 relative error = 334.256413687346 % Correct digits = 0 h = 0.005 Finished! diff ( y , x , 2 ) = sin(x); Iterations = 981 Total Elapsed Time = 1 Minutes 16 Seconds Elapsed Time(since restart) = 1 Minutes 16 Seconds Time to Timeout = 8 Minutes 44 Seconds Percent Done = 100.2 %