##############ECHO OF PROBLEM################# ##############temp/lin_sin_cospostode.ode################# diff ( y , x , 1 ) = sin(2.0 * x + 3.0) + cos(1.5 * 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(2.0*x + 3.0)/2.0 + sin(1.5*x -2.0)/1.5); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = -0.14170274741949 y[1] (numeric) = -0.14170274741949 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) = -0.1777107773452486 y[1] (numeric) = -0.1777107773456152 absolute error = 3.665401315799954e-13 relative error = 2.062565574556559e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = -0.2181433012924979 y[1] (numeric) = -0.2181433012932044 absolute error = 7.064349105689871e-13 relative error = 3.238398366502037e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = -0.2614826307017653 y[1] (numeric) = -0.2614826307027693 absolute error = 1.00403019231976e-12 relative error = 3.839758647161959e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = -0.3058346024719184 y[1] (numeric) = -0.3058346024731637 absolute error = 1.245337166722038e-12 relative error = 4.071930241563769e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = -0.3490078293706074 y[1] (numeric) = -0.3490078293720265 absolute error = 1.419087070075875e-12 relative error = 4.066060846357011e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = -0.3886105682037063 y[1] (numeric) = -0.3886105682052227 absolute error = 1.516342607033039e-12 relative error = 3.901959264880787e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = -0.4221611304654883 y[1] (numeric) = -0.4221611304670196 absolute error = 1.53138612901671e-12 relative error = 3.62749201312815e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = -0.4472070955437499 y[1] (numeric) = -0.4472070955452122 absolute error = 1.462274745733794e-12 relative error = 3.269793257541775e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = -0.4614481184677487 y[1] (numeric) = -0.461448118469059 absolute error = 1.310229702511378e-12 relative error = 2.839386813109202e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = -0.4625591119573782 y[1] (numeric) = -0.4625591119584452 absolute error = 1.067035348967238e-12 relative error = 2.306808624852164e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = -0.4487365373715431 y[1] (numeric) = -0.4487365373723072 absolute error = 7.64110996698264e-13 relative error = 1.702805394840399e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = -0.4192446354435447 y[1] (numeric) = -0.419244635443948 absolute error = 4.032885136950881e-13 relative error = 9.619407849272166e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = -0.3735318794318383 y[1] (numeric) = -0.3735318794318371 absolute error = 1.221245327087672e-15 relative error = 3.269454079649777e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = -0.3116823427497766 y[1] (numeric) = -0.3116823427493435 absolute error = 4.331535130575048e-13 relative error = 1.389727468152558e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = -0.2344513868153343 y[1] (numeric) = -0.2344513868144591 absolute error = 8.751888103120109e-13 relative error = 3.732922300866378e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = -0.1432739587220277 y[1] (numeric) = -0.1432739587207187 absolute error = 1.309063968335522e-12 relative error = 9.136789267303602e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = -0.04024430528854023 y[1] (numeric) = -0.04024430528682372 absolute error = 1.716508879479051e-12 relative error = 4.265221792678914e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 0.07193291693908492 y[1] (numeric) = 0.07193291694116519 absolute error = 2.080266514603579e-12 relative error = 2.891953507689971e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 0.1900189637069348 y[1] (numeric) = 0.190018963709319 absolute error = 2.384148434231292e-12 relative error = 1.254689736077264e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 0.3103424218905404 y[1] (numeric) = 0.3103424218931552 absolute error = 2.614797267597169e-12 relative error = 8.425523174267884e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 0.4289223039760163 y[1] (numeric) = 0.4289223039787776 absolute error = 2.761235684545227e-12 relative error = 6.437612730672137e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 0.5416084334618292 y[1] (numeric) = 0.5416084334646448 absolute error = 2.81563661275186e-12 relative error = 5.198657256414927e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 0.6442339359759477 y[1] (numeric) = 0.6442339359787215 absolute error = 2.773781204723491e-12 relative error = 4.305549661120382e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 0.7327740478970408 y[1] (numeric) = 0.7327740478996765 absolute error = 2.635669460460122e-12 relative error = 3.596837890239324e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 0.8035050754819155 y[1] (numeric) = 0.8035050754843197 absolute error = 2.404187959825776e-12 relative error = 2.992125417980496e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 0.85315720088605 y[1] (numeric) = 0.8531572008881372 absolute error = 2.087219286295294e-12 relative error = 2.446465064266707e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 0.8790549453996528 y[1] (numeric) = 0.8790549454013481 absolute error = 1.695310558602614e-12 relative error = 1.928560401684401e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 0.8792394631161733 y[1] (numeric) = 0.8792394631174155 absolute error = 1.242228542253088e-12 relative error = 1.412844389229778e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 0.8525674385371023 y[1] (numeric) = 0.8525674385378469 absolute error = 7.446265826160925e-13 relative error = 8.733931756692203e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 0.7987821781511866 y[1] (numeric) = 0.798782178151408 absolute error = 2.213784711102562e-13 relative error = 2.771449804033505e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 0.7185534888646237 y[1] (numeric) = 0.7185534888643152 absolute error = 3.084199562408685e-13 relative error = 4.292233786634291e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 0.6134840876951974 y[1] (numeric) = 0.6134840876943731 absolute error = 8.242295734817162e-13 relative error = 1.343522334178658e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 0.4860815435543864 y[1] (numeric) = 0.4860815435530806 absolute error = 1.305733299261647e-12 relative error = 2.686243319821814e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 0.3396960648871244 y[1] (numeric) = 0.3396960648853901 absolute error = 1.73439040906942e-12 relative error = 5.105712395125123e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 0.1784257654501164 y[1] (numeric) = 0.1784257654480234 absolute error = 2.092992446023345e-12 relative error = 1.173032628299693e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 0.006992312989629875 y[1] (numeric) = 0.006992312987263076 absolute error = 2.366799464748048e-12 relative error = 3.384859156416753e-08 % Correct digits = 9 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = -0.1694089581608644 y[1] (numeric) = -0.1694089581634086 absolute error = 2.544270349957856e-12 relative error = 1.501851128522916e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = -0.3452793562970564 y[1] (numeric) = -0.3452793562996739 absolute error = 2.617461802856269e-12 relative error = 7.580707491253462e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = -0.515001600409587 y[1] (numeric) = -0.5150016004121692 absolute error = 2.582267732975652e-12 relative error = 5.01409652110196e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = -0.6730324545943468 y[1] (numeric) = -0.6730324545967855 absolute error = 2.438715895891619e-12 relative error = 3.623474439076631e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = -0.8140962522106743 y[1] (numeric) = -0.8140962522128653 absolute error = 2.191025139097746e-12 relative error = 2.691358832752305e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = -0.9333722114432662 y[1] (numeric) = -0.9333722114451132 absolute error = 1.84696702376641e-12 relative error = 1.978810812152271e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = -1.026668591311429 y[1] (numeric) = -1.026668591312848 absolute error = 1.418642980866025e-12 relative error = 1.381792520850279e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = -1.090577150065303 y[1] (numeric) = -1.090577150066225 absolute error = 9.214851104388799e-13 relative error = 8.449517857436328e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = -1.122602032361318 y[1] (numeric) = -1.12260203236169 absolute error = 3.725908470642025e-13 relative error = 3.318993163414133e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = -1.121258103842333 y[1] (numeric) = -1.121258103842126 absolute error = 2.076117056049043e-13 relative error = 1.851596032113029e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = -1.086134839048032 y[1] (numeric) = -1.086134839047234 absolute error = 7.986944439153376e-13 relative error = 7.353547784319041e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = -1.017923110536949 y[1] (numeric) = -1.017923110535571 absolute error = 1.377564728954894e-12 relative error = 1.353309218245606e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = -0.9184035771495004 y[1] (numeric) = -0.9184035771475766 absolute error = 1.923794457070471e-12 relative error = 2.094715770861278e-10 % Correct digits = 11 h = 0.005 Finished! diff ( y , x , 1 ) = sin(2.0 * x + 3.0) + cos(1.5 * x - 2.0); Iterations = 981 Total Elapsed Time = 56 Seconds Elapsed Time(since restart) = 55 Seconds Time to Timeout = 9 Minutes 4 Seconds Percent Done = 100.2 %