##############ECHO OF PROBLEM################# ##############temp/mtest7postode.ode################# diff ( y2 , x , 5 ) = y1 ; 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 = 0.0; x_end = 5.0; 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); array_y2_init[3 + 1] = exact_soln_y2ppp(x_start); array_y2_init[4 + 1] = exact_soln_y2pppp(x_start); glob_h = 0.00001; glob_look_poles = true; 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_y1 (double x) { return(1.0 + cos(x)); } double exact_soln_y2 (double x) { return(1.0 + sin(x)); } double exact_soln_y2p (double x) { return( cos(x)); } double exact_soln_y2pp (double x) { return( -sin(x)); } double exact_soln_y2ppp (double x) { return( -cos(x)); } double exact_soln_y2pppp (double x) { return( sin(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0 y2[1] (analytic) = 1 y2[1] (numeric) = 1 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 y1[1] (analytic) = 2 y1[1] (numeric) = 2 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 x[1] = 0 y2[1] (analytic) = 1 y2[1] (numeric) = 1 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 y1[1] (analytic) = 2 y1[1] (numeric) = 2 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1 y2[1] (analytic) = 1.099833416646828 y2[1] (numeric) = 1.099833499980101 absolute error = 8.333327317089356e-08 relative error = 7.576899547656955e-06 % Correct digits = 7 h = 0.005 y1[1] (analytic) = 1.995004165278026 y1[1] (numeric) = 1.995004163889107 absolute error = 1.388918313693921e-09 relative error = 6.961982024234822e-08 % Correct digits = 9 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.2000000000000001 y2[1] (analytic) = 1.198669330795061 y2[1] (numeric) = 1.198671997459365 absolute error = 2.666664303818678e-06 relative error = 0.0002224687188792855 % Correct digits = 5 h = 0.005 y1[1] (analytic) = 1.980066577841242 y1[1] (numeric) = 1.980066488952367 absolute error = 8.888887448321725e-08 relative error = 4.489186145454156e-06 % Correct digits = 7 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.3000000000000002 y2[1] (analytic) = 1.29552020666134 y2[1] (numeric) = 1.295540456640486 absolute error = 2.024997914662485e-05 relative error = 0.00156307705912289 % Correct digits = 4 h = 0.005 y1[1] (analytic) = 1.955336489125606 y1[1] (numeric) = 1.955335476626496 absolute error = 1.012499110109033e-06 relative error = 5.178132335482605e-05 % Correct digits = 6 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.4000000000000002 y2[1] (analytic) = 1.389418342308651 y2[1] (numeric) = 1.389503675541604 absolute error = 8.53332329535661e-05 relative error = 0.006141651535402707 % Correct digits = 4 h = 0.005 y1[1] (analytic) = 1.921060994002885 y1[1] (numeric) = 1.921055305120089 absolute error = 5.6888827957291e-06 relative error = 0.0002961323359064859 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5000000000000003 y2[1] (analytic) = 1.479425538604203 y2[1] (numeric) = 1.479685954920629 absolute error = 0.0002604163164261486 relative error = 0.01760252947044865 % Correct digits = 3 h = 0.005 y1[1] (analytic) = 1.877582561890373 y1[1] (numeric) = 1.87756086052793 absolute error = 2.17013624428386e-05 relative error = 0.001155814017626442 % Correct digits = 4 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.6000000000000004 y2[1] (analytic) = 1.564642473395036 y2[1] (numeric) = 1.565290472377262 absolute error = 0.0006479989822265608 relative error = 0.0414151471179548 % Correct digits = 3 h = 0.005 y1[1] (analytic) = 1.825335614909678 y1[1] (numeric) = 1.825270814999354 absolute error = 6.479991032404264e-05 relative error = 0.003550027172797431 % Correct digits = 4 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.7000000000000005 y2[1] (analytic) = 1.644217687237691 y2[1] (numeric) = 1.645618267888433 absolute error = 0.001400580650742 relative error = 0.08518219099655809 % Correct digits = 3 h = 0.005 y1[1] (analytic) = 1.764842187284488 y1[1] (numeric) = 1.764678786157937 absolute error = 0.0001634011265512214 relative error = 0.009258682035623933 % Correct digits = 4 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.8000000000000006 y2[1] (analytic) = 1.717356090899523 y2[1] (numeric) = 1.72008675079412 absolute error = 0.002730659894597309 relative error = 0.1590037097761731 % Correct digits = 2 h = 0.005 y1[1] (analytic) = 1.696706709347165 y1[1] (numeric) = 1.696342621163088 absolute error = 0.0003640881840769605 relative error = 0.02145852209289897 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.9000000000000007 y2[1] (analytic) = 1.783326909627484 y2[1] (numeric) = 1.788247642803854 absolute error = 0.004920733176370096 relative error = 0.2759299570821807 % Correct digits = 2 h = 0.005 y1[1] (analytic) = 1.621609968270664 y1[1] (numeric) = 1.620871857581003 absolute error = 0.0007381106896613421 relative error = 0.04551715295932021 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.000000000000001 y2[1] (analytic) = 1.841470984807897 y2[1] (numeric) = 1.849804276841874 absolute error = 0.008333292033977369 relative error = 0.4525345282508864 % Correct digits = 2 h = 0.005 y1[1] (analytic) = 1.540302305868139 y1[1] (numeric) = 1.538913421518333 absolute error = 0.001388884349806441 relative error = 0.09016959492400703 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.104999999999998 y2[1] (analytic) = 1.893464191149863 y2[1] (numeric) = 1.907192810463295 absolute error = 0.01372861931343183 relative error = 0.725053020680297 % Correct digits = 2 h = 0.005 y1[1] (analytic) = 1.449134433252363 y1[1] (numeric) = 1.446606071764853 absolute error = 0.002528361487510011 relative error = 0.1744739086652911 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.204999999999996 y2[1] (analytic) = 1.933839216726195 y2[1] (numeric) = 1.955010590120104 absolute error = 0.02117137339390851 relative error = 1.094784572098482 % Correct digits = 1 h = 0.005 y1[1] (analytic) = 1.357693049001803 y1[1] (numeric) = 1.353441111012844 absolute error = 0.004251937988959398 relative error = 0.3131737318744828 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.304999999999994 y2[1] (analytic) = 1.964883629535204 y2[1] (numeric) = 1.996423786428589 absolute error = 0.03154015689338507 relative error = 1.605192104982113 % Correct digits = 1 h = 0.005 y1[1] (analytic) = 1.262677714043219 y1[1] (numeric) = 1.255817677368672 absolute error = 0.006860036674546599 relative error = 0.5432927657034575 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.404999999999992 y2[1] (analytic) = 1.98628724406602 y2[1] (numeric) = 2.031910813891365 absolute error = 0.04562356982534466 relative error = 2.296927091569653 % Correct digits = 1 h = 0.005 y1[1] (analytic) = 1.165037790195623 y1[1] (numeric) = 1.154354144702304 absolute error = 0.01068364549331902 relative error = 0.9170213690257298 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.50499999999999 y2[1] (analytic) = 1.997836202477346 y2[1] (numeric) = 2.062176780781227 absolute error = 0.0643405783038804 relative error = 3.22051318441908 % Correct digits = 1 h = 0.005 y1[1] (analytic) = 1.065748863302634 y1[1] (numeric) = 1.049609815347632 absolute error = 0.01613904795500187 relative error = 1.514338744400704 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.604999999999988 y2[1] (analytic) = 1.999415111394314 y2[1] (numeric) = 2.088165536936886 absolute error = 0.08875042554257129 relative error = 4.438819384568929 % Correct digits = 1 h = 0.005 y1[1] (analytic) = 0.9658029955012084 y1[1] (numeric) = 0.9420616398873348 absolute error = 0.02374135561387358 relative error = 2.458198589615358 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.704999999999986 y2[1] (analytic) = 1.991008194880944 y2[1] (numeric) = 2.11107069094693 absolute error = 0.120062496065986 relative error = 6.030236157474246 % Correct digits = 1 h = 0.005 y1[1] (analytic) = 0.8661988128647083 y1[1] (numeric) = 0.8320797834143338 absolute error = 0.03411902945037459 relative error = 3.938937452192473 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.804999999999984 y2[1] (analytic) = 1.972699452068079 y2[1] (numeric) = 2.132345566220406 absolute error = 0.1596461141523269 relative error = 8.092774293872385 % Correct digits = 1 h = 0.005 y1[1] (analytic) = 0.7679315274612719 y1[1] (numeric) = 0.7199021428955233 absolute error = 0.04802938456574857 relative error = 6.254383737119163 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE Complex estimate of poles used x[1] = 1.904999999999981 y2[1] (analytic) = 1.944671817861841 y2[1] (numeric) = 2.15371206965722 absolute error = 0.2090402517953789 relative error = 10.7493845426946 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.6719829935238044 y1[1] (numeric) = 0.6056079230940057 absolute error = 0.06637507042979873 relative error = 9.877492595718117 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.004999999999979 y2[1] (analytic) = 1.907205335118514 y2[1] (numeric) = 2.177168449650234 absolute error = 0.2699631145317205 relative error = 14.15490558676237 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.5793118970870402 y1[1] (numeric) = 0.4890903809727352 absolute error = 0.09022151611430501 relative error = 15.57391045617512 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.104999999999977 y2[1] (analytic) = 1.860674356548896 y2[1] (numeric) = 2.204995921714112 absolute error = 0.3443215651652152 relative error = 18.50520290954345 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.4908441771135841 y1[1] (numeric) = 0.3700288507379163 absolute error = 0.1208153263756678 relative error = 24.61378417202054 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.204999999999975 y2[1] (analytic) = 1.80554380430976 y2[1] (numeric) = 2.239764139875229 absolute error = 0.4342203355654697 relative error = 24.04928279939836 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.4074637738178705 y1[1] (numeric) = 0.2478601638435137 absolute error = 0.1596036099743568 relative error = 39.1700122145575 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.304999999999973 y2[1] (analytic) = 1.742364524655339 y2[1] (numeric) = 2.284335489796415 absolute error = 0.541970965141076 relative error = 31.10548668042265 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.3300037966277331 y1[1] (numeric) = 0.1217495805550053 absolute error = 0.2082542160727278 relative error = 63.10661216654208 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.404999999999971 y2[1] (analytic) = 1.671767784063649 y2[1] (numeric) = 2.341868175167066 absolute error = 0.6701003911034171 relative error = 40.0833415676052 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.2592382000303916 y1[1] (numeric) = -0.009438647724927654 absolute error = 0.2686768477553192 relative error = 103.6409170113899 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.504999999999969 y2[1] (analytic) = 1.594458961830502 y2[1] (numeric) = 2.415818061875299 absolute error = 0.8213591000447971 relative error = 51.51334212464424 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.1958740504750504 y1[1] (numeric) = -0.1471709629910743 absolute error = 0.3430450134661247 relative error = 175.1355080645664 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.604999999999967 y2[1] (analytic) = 1.511210502152752 y2[1] (numeric) = 2.50993923460174 absolute error = 0.9987287324489884 relative error = 66.087995750842 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.1405444615986633 y1[1] (numeric) = -0.2932743056359306 absolute error = 0.4338187672345939 relative error = 308.6701263785125 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.704999999999965 y2[1] (analytic) = 1.422854196121216 y2[1] (numeric) = 2.628283207438843 absolute error = 1.205429011317626 relative error = 84.71908187105161 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.09380226836375276 y1[1] (numeric) = -0.4499659083604334 absolute error = 0.5437681767241861 relative error = 579.6961909444718 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.804999999999962 y2[1] (analytic) = 1.330272870739051 y2[1] (numeric) = 2.775196713647886 absolute error = 1.444923842908835 relative error = 108.6186056027804 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.05611450331420715 y1[1] (numeric) = -0.6198829408059703 absolute error = 0.6759974441201775 relative error = 1204.675091455416 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.90499999999996 y2[1] (analytic) = 1.234391568006158 y2[1] (numeric) = 2.955317979420262 absolute error = 1.720926411414104 relative error = 139.4149519502808 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.02785773014048269 y1[1] (numeric) = -0.8061118582499024 absolute error = 0.833969588390385 relative error = 2993.673871434576 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.004999999999958 y2[1] (analytic) = 1.136168302205299 y2[1] (numeric) = 3.173571362213056 absolute error = 2.037403060007758 relative error = 179.3222937176795 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.009314281179683871 y1[1] (numeric) = -1.012217297013659 absolute error = 1.021531578193343 relative error = 10967.36890895551 % Correct digits = -2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.104999999999956 y2[1] (analytic) = 1.03658448774006 y2[1] (numeric) = 3.435160205586668 absolute error = 2.398575717846608 relative error = 231.3922064448343 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.0006694364441777027 y1[1] (numeric) = -1.24227034589479 absolute error = 1.242939782338968 relative error = 185669.5722423245 % Correct digits = -3 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 3.204999999999954 y2[1] (analytic) = 0.9366351331665469 y2[1] (numeric) = 3.745557729192939 absolute error = 2.808922596026392 relative error = 299.895070829777 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.002009572364955621 y1[1] (numeric) = -1.500876006503002 absolute error = 1.502885578867958 relative error = 74786.33788344053 % Correct digits = -2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used x[1] = 3.304999999999952 y2[1] (analytic) = 0.8373188993967933 y2[1] (numeric) = 4.110495734360565 absolute error = 3.273176834963771 relative error = 390.9116153142818 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.01332129874688725 y1[1] (numeric) = -1.793199635377175 absolute error = 1.806520934124062 relative error = 13561.14721581622 % Correct digits = -2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.40499999999995 y2[1] (analytic) = 0.7396281214090444 y2[1] (numeric) = 4.535950862321729 absolute error = 3.796322740912685 relative error = 513.2745268906783 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.03449159255912395 y1[1] (numeric) = -2.124992136679362 absolute error = 2.159483729238486 relative error = 6260.898871331601 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.504999999999947 y2[1] (analytic) = 0.6445388931646763 y2[1] (numeric) = 5.028128093250746 absolute error = 4.383589200086069 relative error = 680.1124410914463 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.06530892722386258 y1[1] (numeric) = -2.50261364556919 absolute error = 2.567922572793052 relative error = 3931.962569207207 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.604999999999945 y2[1] (analytic) = 0.5530013147999866 y2[1] (numeric) = 5.593441119683933 absolute error = 5.040439804883947 relative error = 911.469768694313 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.1054653861199896 y1[1] (numeric) = -2.933055408497864 absolute error = 3.038520794617854 relative error = 2881.059754677125 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.704999999999943 y2[1] (analytic) = 0.4659299995396949 y2[1] (numeric) = 6.238489167316026 absolute error = 5.772559167776332 relative error = 1238.932709522719 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 0.1545597391841753 y1[1] (numeric) = -3.423959527039954 absolute error = 3.578519266224129 relative error = 2315.298463308042 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.804999999999941 y2[1] (analytic) = 0.3841949351839317 y2[1] (numeric) = 6.970029769394275 absolute error = 6.585834834210343 relative error = 1714.190956488639 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 0.212101451869038 y1[1] (numeric) = -3.983636185894497 absolute error = 4.195737637763536 relative error = 1978.174878479471 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.904999999999939 y2[1] (analytic) = 0.3086127914777196 y2[1] (numeric) = 7.794946927749571 absolute error = 7.486334136271851 relative error = 2425.801633310565 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 0.2775155864021918 y1[1] (numeric) = -4.621077932704248 absolute error = 4.89859351910644 relative error = 1765.159781694968 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.004999999999937 y2[1] (analytic) = 0.2399387602168361 y2[1] (numeric) = 8.720214013729562 absolute error = 8.480275253512726 relative error = 3534.349867378234 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 0.3501485463744196 y1[1] (numeric) = -5.345970516712686 absolute error = 5.696119063087106 relative error = 1626.772157721926 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.104999999999935 y2[1] (analytic) = 0.1788590096210234 y2[1] (numeric) = 9.752850675774983 absolute error = 9.57399166615396 relative error = 5352.814871579507 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 0.4292746072589433 y1[1] (numeric) = -6.168699724335557 absolute error = 6.5979743315945 relative error = 1537.005501845239 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.204999999999933 y2[1] (analytic) = 0.1259838283679535 y2[1] (numeric) = 10.89987292698179 absolute error = 10.77388909861384 relative error = 8551.803226003884 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 0.5141031676110031 y1[1] (numeric) = -7.100353571785647 absolute error = 7.61445673939665 relative error = 1481.11453480834 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.30499999999993 y2[1] (analytic) = 0.08184152779049592 y2[1] (numeric) = 12.16823548563083 absolute error = 12.08639395784033 relative error = 14768.04537273545 % Correct digits = -2 h = 0.005 y1[1] (analytic) = 0.6037866484961552 y1[1] (numeric) = -8.152719127263945 absolute error = 8.7565057757601 relative error = 1450.2648903499 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.404999999999928 y2[1] (analytic) = 0.0468731631645161 y2[1] (numeric) = 13.56476533429826 absolute error = 13.51789217113374 relative error = 28839.30005681173 % Correct digits = -2 h = 0.005 y1[1] (analytic) = 0.6974289622188125 y1[1] (numeric) = -9.338273137218561 absolute error = 10.03570209943737 relative error = 1438.95688924498 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.504999999999926 y2[1] (analytic) = 0.02142812683035223 y2[1] (numeric) = 15.09608534879075 absolute error = 15.07465722196039 relative error = 70349.85998219704 % Correct digits = -2 h = 0.005 y1[1] (analytic) = 0.7940944657342917 y1[1] (numeric) = -10.67016552207384 absolute error = 11.46425998780813 relative error = 1443.689697195816 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.604999999999924 y2[1] (analytic) = 0.00576065718004454 y2[1] (numeric) = 16.76852672684103 absolute error = 16.76276606966098 relative error = 290987.0444595937 % Correct digits = -3 h = 0.005 y1[1] (analytic) = 0.8928173092848333 y1[1] (numeric) = -12.16219468594839 absolute error = 13.05501199523322 relative error = 1462.226578659254 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.704999999999922 y2[1] (analytic) = 2.729839136197677e-05 y2[1] (numeric) = 18.58802881838442 absolute error = 18.58800151999305 relative error = 68091929.93651561 % Correct digits = -5 h = 0.005 y1[1] (analytic) = 0.9926110868511139 y1[1] (numeric) = -13.82877345152471 absolute error = 14.82138453837582 relative error = 1493.171367387613 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.80499999999992 y2[1] (analytic) = 0.004285336290124616 y2[1] (numeric) = 20.56002482451994 absolute error = 20.55573948822982 relative error = 479676.228341745 % Correct digits = -3 h = 0.005 y1[1] (analytic) = 1.092478691995128 y1[1] (numeric) = -15.68488428473298 absolute error = 16.7773629767281 relative error = 1535.715350757882 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.904999999999918 y2[1] (analytic) = 0.01849222596916822 y2[1] (numeric) = 22.68931169123751 absolute error = 22.67081946526834 relative error = 122596.4873188713 % Correct digits = -3 h = 0.005 y1[1] (analytic) = 1.191422280618118 y1[1] (numeric) = -17.74602231362217 absolute error = 18.93744459424029 relative error = 1589.482159458644 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 5.004999999999916 y2[1] (analytic) = 0.04250601688299314 y2[1] (numeric) = 24.97990237705868 absolute error = 24.93739636017569 relative error = 58667.92089416701 % Correct digits = -2 h = 0.005 y1[1] (analytic) = 1.288453241088966 y1[1] (numeric) = -20.02812447110027 absolute error = 21.31657771218924 relative error = 1654.431610895949 % Correct digits = -1 h = 0.005 Finished! diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * y2 + 1.0; Iterations = 1001 Total Elapsed Time Unknown Elapsed Time(since restart) Unknown Time to Timeout = 21 Minutes 3 Seconds Percent Done = 100.2 %