##############ECHO OF PROBLEM################# ##############temp/mtest4postode.ode################# diff ( y2 , x , 3 ) = m1 * cos(x) ; diff ( y1 , x , 1 ) = m1 * y2 + 1.0; ! // 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; glob_h = 0.00001; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); array_y2_init[1 + 1] = exact_soln_y2p(x_start); array_y2_init[2 + 1] = exact_soln_y2pp(x_start); glob_max_iter = 20; // 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_y2 (double x) { return(1.0 + cos(x)); } double exact_soln_y2p (double x) { return( -sin(x)); } double exact_soln_y2pp (double x) { return( -cos(x)); } double exact_soln_y1 (double x) { return( 1.0 - sin(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y2[1] (analytic) = 1.995004165278026 y2[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 y1[1] (analytic) = 0.9001665833531718 y1[1] (numeric) = 0.9001665833531718 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 x[1] = 0.1 y2[1] (analytic) = 1.995004165278026 y2[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 y1[1] (analytic) = 0.9001665833531718 y1[1] (numeric) = 0.9001665833531718 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.2000000000000001 y2[1] (analytic) = 1.980066577841242 y2[1] (numeric) = 1.979880467490627 absolute error = 0.0001861103506148876 relative error = 0.009399196607711722 % Correct digits = 4 h = 0.005 y1[1] (analytic) = 0.8013306692049387 y1[1] (numeric) = 0.8013353040876487 absolute error = 4.634882710075061e-06 relative error = 0.0005783982678054344 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.3000000000000002 y2[1] (analytic) = 1.955336489125606 y2[1] (numeric) = 1.953820023935036 absolute error = 0.001516465190569694 relative error = 0.07755520336286628 % Correct digits = 3 h = 0.005 y1[1] (analytic) = 0.7044797933386603 y1[1] (numeric) = 0.7045550701111504 absolute error = 7.527677249008491e-05 relative error = 0.01068544097387582 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.4000000000000002 y2[1] (analytic) = 1.921060994002885 y2[1] (numeric) = 1.915855132674361 absolute error = 0.005205861328523964 relative error = 0.2709888621327213 % Correct digits = 2 h = 0.005 y1[1] (analytic) = 0.6105816576913493 y1[1] (numeric) = 0.6109681470440611 absolute error = 0.0003864893527117941 relative error = 0.06329855275593056 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5000000000000003 y2[1] (analytic) = 1.877582561890373 y2[1] (numeric) = 1.865047594575977 absolute error = 0.01253496731439574 relative error = 0.6676120437428533 % Correct digits = 2 h = 0.005 y1[1] (analytic) = 0.5205744613957967 y1[1] (numeric) = 0.5218121750522786 absolute error = 0.001237713656481954 relative error = 0.237759196477545 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.6000000000000004 y2[1] (analytic) = 1.825335614909678 y2[1] (numeric) = 1.800498087487134 absolute error = 0.0248375274225443 relative error = 1.36071017404508 % Correct digits = 1 h = 0.005 y1[1] (analytic) = 0.4353575266049643 y1[1] (numeric) = 0.4384167470059975 absolute error = 0.003059220401033236 relative error = 0.7026915153827392 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.7000000000000005 y2[1] (analytic) = 1.764842187284488 y2[1] (numeric) = 1.72135515196463 absolute error = 0.0434870353198582 relative error = 2.464075010965737 % Correct digits = 1 h = 0.005 y1[1] (analytic) = 0.3557823127623085 y1[1] (numeric) = 0.3621990678774659 absolute error = 0.00641675511515738 relative error = 1.80356214600367 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.8000000000000006 y2[1] (analytic) = 1.696706709347165 y2[1] (numeric) = 1.626823698776113 absolute error = 0.06988301057105173 relative error = 4.118744281852951 % Correct digits = 1 h = 0.005 y1[1] (analytic) = 0.2826439091004768 y1[1] (numeric) = 0.2946587387475801 absolute error = 0.01201482964710326 relative error = 4.2508715950543 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.9000000000000007 y2[1] (analytic) = 1.621609968270664 y2[1] (numeric) = 1.516172953168869 absolute error = 0.1054370151017947 relative error = 6.501995989469408 % Correct digits = 1 h = 0.005 y1[1] (analytic) = 0.2166730903725162 y1[1] (numeric) = 0.2373717175377979 absolute error = 0.02069862716528173 relative error = 9.552929313785814 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.000000000000001 y2[1] (analytic) = 1.540302305868139 y2[1] (numeric) = 1.388743756529587 absolute error = 0.1515585493385516 relative error = 9.839532717775864 % Correct digits = 1 h = 0.005 y1[1] (analytic) = 0.1585290151921031 y1[1] (numeric) = 0.1919835168097413 absolute error = 0.03345450161763816 relative error = 21.10307792999186 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.104999999999998 y2[1] (analytic) = 1.449134433252363 y2[1] (numeric) = 1.236250752281129 absolute error = 0.2128836809712342 relative error = 14.69040249726515 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.1065358088501371 y1[1] (numeric) = 0.1590011732160415 absolute error = 0.05246536436590442 relative error = 49.24669454540579 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.204999999999996 y2[1] (analytic) = 1.357693049001803 y2[1] (numeric) = 1.072701505695834 absolute error = 0.2849915433059687 relative error = 20.99086708262216 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.06616078327380481 y1[1] (numeric) = 0.1434027488980663 absolute error = 0.0772419656242615 relative error = 116.7488681392986 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.304999999999994 y2[1] (analytic) = 1.262677714043219 y2[1] (numeric) = 0.8908699388600172 absolute error = 0.3718077751832018 relative error = 29.44597588506069 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.035116370464796 y1[1] (numeric) = 0.145070386462395 absolute error = 0.109954015997599 relative error = 313.1132703700895 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.404999999999992 y2[1] (analytic) = 1.165037790195623 y2[1] (numeric) = 0.6904458662632721 absolute error = 0.4745919239323514 relative error = 40.73618280250479 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.01371275593397977 y1[1] (numeric) = 0.1658486184763366 absolute error = 0.1521358625423568 relative error = 1109.447752696954 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.50499999999999 y2[1] (analytic) = 1.065748863302634 y2[1] (numeric) = 0.4712154300647793 absolute error = 0.5945334332378542 relative error = 55.78550948630274 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.002163797522653718 y1[1] (numeric) = 0.2076082015317584 absolute error = 0.2054444040091046 relative error = 9494.622387641155 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.604999999999988 y2[1] (analytic) = 0.9658029955012084 y2[1] (numeric) = 0.2330632368901568 absolute error = 0.7327397586110516 relative error = 75.86844957245059 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.0005848886056857181 y1[1] (numeric) = 0.2722363685138209 absolute error = 0.2716514799081352 relative error = 46444.99435745605 % Correct digits = -2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.704999999999986 y2[1] (analytic) = 0.8661988128647083 y2[1] (numeric) = -0.02402648919608643 absolute error = 0.8902253020607948 relative error = 102.7737845907022 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.008991805119056217 y1[1] (numeric) = 0.3616269162440374 absolute error = 0.3526351111249811 relative error = 3921.738810571485 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.804999999999984 y2[1] (analytic) = 0.7679315274612719 y2[1] (numeric) = -0.299969749062618 absolute error = 1.06790127652389 relative error = 139.0620437285987 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.02730054793192075 y1[1] (numeric) = 0.47767022753865 absolute error = 0.4503696796067292 relative error = 1649.67267591044 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.904999999999981 y2[1] (analytic) = 0.6719829935238044 y2[1] (numeric) = -0.5945836078028363 absolute error = 1.266566601326641 relative error = 188.4819427772875 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.05532818213815891 y1[1] (numeric) = 0.6222433273786195 absolute error = 0.5669151452404606 relative error = 1024.640831005125 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.004999999999979 y2[1] (analytic) = 0.5793118970870402 y2[1] (numeric) = -0.9075880225599864 absolute error = 1.486899919647027 relative error = 256.6665602974184 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.09279466488148617 y1[1] (numeric) = 0.7972000725466879 absolute error = 0.7044054076652018 relative error = 759.1011924714007 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.104999999999977 y2[1] (analytic) = 0.4908441771135841 y2[1] (numeric) = -1.238608640622816 absolute error = 1.7294528177364 relative error = 352.3425352433579 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.1393256434511037 y1[1] (numeric) = 1.004361572753421 absolute error = 0.8650359293023175 relative error = 620.8734500522166 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.204999999999975 y2[1] (analytic) = 0.4074637738178705 y2[1] (numeric) = -1.58718053983412 absolute error = 1.99464431365199 relative error = 489.5267854029062 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.1944561956902404 y1[1] (numeric) = 1.245506938961171 absolute error = 1.05105074327093 relative error = 540.5077166814499 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.304999999999973 y2[1] (analytic) = 0.3300037966277331 y2[1] (numeric) = -1.952752873939253 absolute error = 2.282756670566986 relative error = 691.736487244749 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.2576354753446606 y1[1] (numeric) = 1.522364451345644 absolute error = 1.264728976000984 relative error = 490.8986133641144 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.404999999999971 y2[1] (analytic) = 0.2592382000303916 y2[1] (numeric) = -2.334694376459823 absolute error = 2.593932576490214 relative error = 1000.598127971154 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 0.3282322159363506 y1[1] (numeric) = 1.836603235141899 absolute error = 1.508371019205548 relative error = 459.5438674118586 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.504999999999969 y2[1] (analytic) = 0.1958740504750504 y2[1] (numeric) = -2.732299668099668 absolute error = 2.928173718574718 relative error = 1494.926822349904 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 0.405541038169498 y1[1] (numeric) = 2.189825527546935 absolute error = 1.784284489377437 relative error = 439.9763085460381 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.604999999999967 y2[1] (analytic) = 0.1405444615986633 y2[1] (numeric) = -3.144796304661624 absolute error = 3.285340766260287 relative error = 2337.581096323709 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 0.4887894978472484 y1[1] (numeric) = 2.583559612945475 absolute error = 2.094770115098227 relative error = 428.5628321238733 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.704999999999965 y2[1] (analytic) = 0.09380226836375276 y2[1] (numeric) = -3.5713524950546 absolute error = 3.665154763418353 relative error = 3907.319969284078 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 0.5771458038787838 y1[1] (numeric) = 3.019253497047778 absolute error = 2.442107693168995 relative error = 423.1353111737954 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.804999999999962 y2[1] (analytic) = 0.05611450331420715 y2[1] (numeric) = -4.01108541227521 absolute error = 4.067199915589417 relative error = 7248.03691625954 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 0.6697271292609487 y1[1] (numeric) = 3.498269383145442 absolute error = 2.828542253884494 relative error = 422.3424929800621 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.90499999999996 y2[1] (analytic) = 0.02785773014048269 y2[1] (numeric) = -4.463070014323367 absolute error = 4.49092774446385 relative error = 16120.93922159745 % Correct digits = -2 h = 0.005 y1[1] (analytic) = 0.7656084319938419 y1[1] (numeric) = 4.021879005676614 absolute error = 3.256270573682772 relative error = 425.3180134396644 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.004999999999958 y2[1] (analytic) = 0.009314281179683871 y2[1] (numeric) = -4.926348286916173 absolute error = 4.935662568095856 relative error = 52990.26809348882 % Correct digits = -2 h = 0.005 y1[1] (analytic) = 0.8638316977947014 y1[1] (numeric) = 4.591259867726073 absolute error = 3.727428169931372 relative error = 431.4993510248838 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.104999999999956 y2[1] (analytic) = 0.0006694364441777027 y2[1] (numeric) = -5.399938815649942 absolute error = 5.40060825209412 relative error = 806739.5044092523 % Correct digits = -3 h = 0.005 y1[1] (analytic) = 0.9634155122599398 y1[1] (numeric) = 5.207492420053851 absolute error = 4.244076907793911 relative error = 440.5240370106075 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.204999999999954 y2[1] (analytic) = 0.002009572364955621 y2[1] (numeric) = -5.88284659196853 absolute error = 5.884856164333486 relative error = 292841.2167164453 % Correct digits = -3 h = 0.005 y1[1] (analytic) = 1.063364866833453 y1[1] (numeric) = 5.871558209838592 absolute error = 4.808193343005139 relative error = 452.1677829476578 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.304999999999952 y2[1] (analytic) = 0.01332129874688725 y2[1] (numeric) = -6.374072954959908 absolute error = 6.387394253706795 relative error = 47948.73514265504 % Correct digits = -2 h = 0.005 y1[1] (analytic) = 1.162681100603207 y1[1] (numeric) = 6.584339017632823 absolute error = 5.421657917029616 relative error = 466.3065318785025 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.40499999999995 y2[1] (analytic) = 0.03449159255912395 y2[1] (numeric) = -6.872625569645882 absolute error = 6.907117162205005 relative error = 20025.50955095835 % Correct digits = -2 h = 0.005 y1[1] (analytic) = 1.260371878590955 y1[1] (numeric) = 7.346616991153351 absolute error = 6.086245112562395 relative error = 482.8928045718196 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.504999999999947 y2[1] (analytic) = 0.06530892722386258 y2[1] (numeric) = -7.377528342065185 absolute error = 7.442837269289048 relative error = 11396.35511662421 % Correct digits = -2 h = 0.005 y1[1] (analytic) = 1.355461106835324 y1[1] (numeric) = 8.159075774570036 absolute error = 6.803614667734712 relative error = 501.9409729593436 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.604999999999945 y2[1] (analytic) = 0.1054653861199896 y2[1] (numeric) = -7.887831172081664 absolute error = 7.993296558201654 relative error = 7579.071060440208 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.446998685200013 y1[1] (numeric) = 9.022302622009445 absolute error = 7.575303936809432 relative error = 523.5183704235587 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.704999999999943 y2[1] (analytic) = 0.1545597391841753 y2[1] (numeric) = -8.402619446470792 absolute error = 8.557179185654968 relative error = 5536.486559063176 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.534070000460305 y1[1] (numeric) = 9.936791474155942 absolute error = 8.402721473695637 relative error = 547.7404206570991 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.804999999999941 y2[1] (analytic) = 0.212101451869038 y2[1] (numeric) = -8.921023177432684 absolute error = 9.133124629301722 relative error = 4306.017025730201 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.615805064816068 y1[1] (numeric) = 10.90294696720987 absolute error = 9.287141902393797 relative error = 574.768708467378 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.904999999999939 y2[1] (analytic) = 0.2775155864021918 y2[1] (numeric) = -9.442225695222591 absolute error = 9.719741281624783 relative error = 3502.412750085455 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.691387208522281 y1[1] (numeric) = 11.92108933414656 absolute error = 10.22970212562428 relative error = 604.8113686848617 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.004999999999937 y2[1] (analytic) = 0.3501485463744196 y2[1] (numeric) = -9.965471808045063 absolute error = 10.31562035441948 relative error = 2946.069735611246 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.760061239783164 y1[1] (numeric) = 12.9914601493046 absolute error = 11.23139890952143 relative error = 638.1254615268454 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.104999999999935 y2[1] (analytic) = 0.4292746072589433 y2[1] (numeric) = -10.4900753476807 absolute error = 10.91934995493965 relative error = 2543.674787722296 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.821140990378977 y1[1] (numeric) = 14.11422885890499 absolute error = 12.29308786852602 relative error = 675.02120557771 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.204999999999933 y2[1] (analytic) = 0.5141031676110031 y2[1] (numeric) = -11.01542602545223 absolute error = 11.52952919306323 relative error = 2242.648931077404 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.874016171632046 y1[1] (numeric) = 15.28950003225083 absolute error = 13.41548386061879 relative error = 715.8680946139053 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.30499999999993 y2[1] (analytic) = 0.6037866484961552 y2[1] (numeric) = -11.5409955300272 absolute error = 12.14478217852335 relative error = 2011.436027737981 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.918158472209504 y1[1] (numeric) = 16.51732126115555 absolute error = 14.59916278894605 relative error = 761.103057982975 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.404999999999928 y2[1] (analytic) = 0.6974289622188125 y2[1] (numeric) = -12.06634280613016 absolute error = 12.76377176834897 relative error = 1830.117827017406 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.953126836835484 y1[1] (numeric) = 17.7976916286715 absolute error = 15.84456479183602 relative error = 811.2409544025247 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.504999999999926 y2[1] (analytic) = 0.7940944657342917 y2[1] (numeric) = -12.59111846142126 absolute error = 13.38521292715555 relative error = 1685.594536259407 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.978571873169648 y1[1] (numeric) = 19.13057066250197 absolute error = 17.15199878933232 relative error = 866.8878306581319 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.604999999999924 y2[1] (analytic) = 0.8928173092848333 y2[1] (numeric) = -13.11506825750892 absolute error = 14.00788556679375 relative error = 1568.953180132045 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.994239342819955 y1[1] (numeric) = 20.51588768363721 absolute error = 18.52164834081725 relative error = 928.7575439478945 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.704999999999922 y2[1] (analytic) = 0.9926110868511139 y2[1] (numeric) = -13.63803565021584 absolute error = 14.63064673706695 relative error = 1473.95560364736 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.999972701608638 y1[1] (numeric) = 21.95355145680595 absolute error = 19.95357875519732 relative error = 997.6925554607848 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.80499999999992 y2[1] (analytic) = 1.092478691995128 y2[1] (numeric) = -14.15996335371671 absolute error = 15.25244204571184 relative error = 1396.13176508342 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.995714663709875 y1[1] (numeric) = 23.44346004631832 absolute error = 21.44774538260845 relative error = 1074.689973101605 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.904999999999918 y2[1] (analytic) = 1.191422280618118 y2[1] (numeric) = -14.68089391291917 absolute error = 15.87231619353729 relative error = 1332.215827397706 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.981507774030832 y1[1] (numeric) = 24.98551077882372 absolute error = 23.00400300479289 relative error = 1160.934279757963 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 5.004999999999916 y2[1] (analytic) = 1.288453241088966 y2[1] (numeric) = -15.20096927836921 absolute error = 16.48942251945817 relative error = 1279.784317630476 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.957493983117007 y1[1] (numeric) = 26.57961021343923 absolute error = 24.62211623032222 relative error = 1257.838667330936 % Correct digits = -1 h = 0.005 Finished! diff ( y2 , x , 3 ) = m1 * cos(x) ; diff ( y1 , x , 1 ) = m1 * y2 + 1.0; Iterations = 981 Total Elapsed Time Unknown Elapsed Time(since restart) Unknown Time to Timeout = 21 Minutes 56 Seconds Percent Done = 100.2 %