##############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_desired_digits_correct=10; glob_display_interval=0.001; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; // 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 Optimize min_size = 0 min_size = 1 opt_iter = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 5 estimated_steps = 5000 step_error = 2e-14 est_needed_step_err = 2e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 4.134535541136002e-65 value3 = 1.587661589912727e-59 max_value3 = 1.587661589912727e-59 value3 = 1.587661589912727e-59 best_h = 0.001 START of Soultion x[1] = 0 y2[1] (analytic) = 1 y2[1] (numeric) = 1 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 y1[1] (analytic) = 2 y1[1] (numeric) = 2 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 x[1] = 0 y2[1] (analytic) = 1 y2[1] (numeric) = 1 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 y1[1] (analytic) = 2 y1[1] (numeric) = 2 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.001 y2[1] (analytic) = 1.000999999833333 y2[1] (numeric) = 1.000999999833333 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 y1[1] (analytic) = 1.999999500000042 y1[1] (numeric) = 1.999999500000042 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.002 y2[1] (analytic) = 1.001999998666667 y2[1] (numeric) = 1.001999998666667 absolute error = 2.220446049250313e-16 relative error = 2.216014024156684e-14 % Correct digits = 15 h = 0.001 y1[1] (analytic) = 1.999998000000667 y1[1] (numeric) = 1.999998000000667 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.003 y2[1] (analytic) = 1.002999995500002 y2[1] (numeric) = 1.002999995500004 absolute error = 2.220446049250313e-15 relative error = 2.2138046452766e-13 % Correct digits = 14 h = 0.001 y1[1] (analytic) = 1.999995500003375 y1[1] (numeric) = 1.999995500003375 absolute error = 2.220446049250313e-16 relative error = 1.110225522630709e-14 % Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.004 y2[1] (analytic) = 1.003999989333342 y2[1] (numeric) = 1.00399998933335 absolute error = 8.659739592076221e-15 relative error = 8.625238729162047e-13 % Correct digits = 14 h = 0.001 y1[1] (analytic) = 1.999992000010667 y1[1] (numeric) = 1.999992000010667 absolute error = 2.220446049250313e-16 relative error = 1.110227465529098e-14 % Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.005 y2[1] (analytic) = 1.004999979166693 y2[1] (numeric) = 1.004999979166719 absolute error = 2.597921877622866e-14 relative error = 2.584996946743186e-12 % Correct digits = 13 h = 0.001 y1[1] (analytic) = 1.999987500026042 y1[1] (numeric) = 1.999987500026042 absolute error = 2.220446049250313e-16 relative error = 1.110229963547973e-14 % Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.006 y2[1] (analytic) = 1.005999964000065 y2[1] (numeric) = 1.00599996400013 absolute error = 6.483702463810914e-14 relative error = 6.445032500826707e-12 % Correct digits = 13 h = 0.001 y1[1] (analytic) = 1.999982000054 y1[1] (numeric) = 1.999982000054 absolute error = 2.220446049250313e-16 relative error = 1.110233016692331e-14 % Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.007 y2[1] (analytic) = 1.006999942833473 y2[1] (numeric) = 1.006999942833613 absolute error = 1.398881011027697e-13 relative error = 1.389156991500474e-11 % Correct digits = 12 h = 0.001 y1[1] (analytic) = 1.999975500100041 y1[1] (numeric) = 1.999975500100041 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.008 y2[1] (analytic) = 1.00799991466694 y2[1] (numeric) = 1.007999914667213 absolute error = 2.728928194528635e-13 relative error = 2.707270263440765e-11 % Correct digits = 12 h = 0.001 y1[1] (analytic) = 1.999968000170666 y1[1] (numeric) = 1.999968000170666 absolute error = 2.220446049250313e-16 relative error = 1.11024078838303e-14 % Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.009000000000000001 y2[1] (analytic) = 1.008999878500492 y2[1] (numeric) = 1.008999878500984 absolute error = 4.920508445138694e-13 relative error = 4.876619462483209e-11 % Correct digits = 12 h = 0.001 y1[1] (analytic) = 1.999959500273374 y1[1] (numeric) = 1.999959500273374 absolute error = 6.661338147750939e-16 relative error = 3.330736520834747e-14 % Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.01 y2[1] (analytic) = 1.009999833334167 y2[1] (numeric) = 1.009999833335 absolute error = 8.333334022836425e-13 relative error = 8.2508271267004e-11 % Correct digits = 12 h = 0.001 y1[1] (analytic) = 1.999950000416665 y1[1] (numeric) = 1.999950000416664 absolute error = 1.332267629550188e-15 relative error = 6.66150468398023e-14 % Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.011 y2[1] (analytic) = 1.010999778168009 y2[1] (numeric) = 1.010999778169351 absolute error = 1.342259636771814e-12 relative error = 1.327655718386079e-10 % Correct digits = 11 h = 0.001 y1[1] (analytic) = 1.999939500610039 y1[1] (numeric) = 1.999939500610037 absolute error = 2.220446049250313e-15 relative error = 1.110256609548945e-13 % Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.012 y2[1] (analytic) = 1.011999712002074 y2[1] (numeric) = 1.011999712004147 absolute error = 2.073674565394867e-12 relative error = 2.049086122062669e-10 % Correct digits = 11 h = 0.001 y1[1] (analytic) = 1.999928000863996 y1[1] (numeric) = 1.999928000863992 absolute error = 3.996802888650564e-15 relative error = 1.998473388503932e-13 % Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.013 y2[1] (analytic) = 1.012999633836427 y2[1] (numeric) = 1.012999633839522 absolute error = 3.094413614235236e-12 relative error = 3.054703586136638e-10 % Correct digits = 11 h = 0.001 y1[1] (analytic) = 1.999915501190035 y1[1] (numeric) = 1.999915501190028 absolute error = 6.439293542825908e-15 relative error = 3.219782805320652e-13 % Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.01400000000000001 y2[1] (analytic) = 1.013999542671149 y2[1] (numeric) = 1.013999542675631 absolute error = 4.481970350411757e-12 relative error = 4.420091096495997e-10 % Correct digits = 11 h = 0.001 y1[1] (analytic) = 1.999902001600656 y1[1] (numeric) = 1.999902001600646 absolute error = 1.021405182655144e-14 relative error = 5.107276165720344e-13 % Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.01500000000000001 y2[1] (analytic) = 1.014999437506328 y2[1] (numeric) = 1.014999437512656 absolute error = 6.328271240363392e-12 relative error = 6.234753445687441e-10 % Correct digits = 11 h = 0.001 y1[1] (analytic) = 1.999887502109359 y1[1] (numeric) = 1.999887502109343 absolute error = 1.576516694967722e-14 relative error = 7.883026886786926e-13 % Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.01600000000000001 y2[1] (analytic) = 1.015999317342071 y2[1] (numeric) = 1.01599931735081 absolute error = 8.738343382219682e-12 relative error = 8.600737454312301e-10 % Correct digits = 11 h = 0.001 y1[1] (analytic) = 1.999872002730643 y1[1] (numeric) = 1.99987200273062 absolute error = 2.331468351712829e-14 relative error = 1.165808786027016e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.01700000000000001 y2[1] (analytic) = 1.016999181178499 y2[1] (numeric) = 1.016999181190331 absolute error = 1.183231290724507e-11 relative error = 1.163453533318855e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 1.999855503480008 y1[1] (numeric) = 1.999855503479975 absolute error = 3.352873534367973e-14 relative error = 1.676557895574724e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.01800000000000001 y2[1] (analytic) = 1.017999028015746 y2[1] (numeric) = 1.017999028031493 absolute error = 1.574651520286352e-11 relative error = 1.546810435915265e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 1.999838004373953 y1[1] (numeric) = 1.999838004373905 absolute error = 4.729550084903167e-14 relative error = 2.364966599574023e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.01900000000000001 y2[1] (analytic) = 1.018998856853967 y2[1] (numeric) = 1.018998856874602 absolute error = 2.063416104647331e-11 relative error = 2.024944474440209e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 1.999819505429976 y1[1] (numeric) = 1.999819505429911 absolute error = 6.550315845288424e-14 relative error = 3.275453523431884e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.02000000000000001 y2[1] (analytic) = 1.019998666693333 y2[1] (numeric) = 1.01999866672 absolute error = 2.666666887307656e-11 relative error = 2.614382718707416e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 1.999800006666578 y1[1] (numeric) = 1.999800006666489 absolute error = 8.903988657493755e-14 relative error = 4.452439557861396e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.02100000000000001 y2[1] (analytic) = 1.020998456534034 y2[1] (numeric) = 1.020998456568068 absolute error = 3.403433090909402e-11 relative error = 3.333436078310029e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 1.999779508103256 y1[1] (numeric) = 1.999779508103137 absolute error = 1.192379528447418e-13 relative error = 5.962554989766658e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.02200000000000001 y2[1] (analytic) = 1.02199822537628 y2[1] (numeric) = 1.021998225419227 absolute error = 4.294697930617986e-11 relative error = 4.202255761292307e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 1.999758009760509 y1[1] (numeric) = 1.999758009760352 absolute error = 1.576516694967722e-13 relative error = 7.883537344383613e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.02300000000000001 y2[1] (analytic) = 1.022997972220302 y2[1] (numeric) = 1.022997972273938 absolute error = 5.363620658727086e-11 relative error = 5.243041339647966e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 1.999735511659836 y1[1] (numeric) = 1.99973551165963 absolute error = 2.05835348765504e-13 relative error = 1.029312864453034e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.02400000000000001 y2[1] (analytic) = 1.023997696066354 y2[1] (numeric) = 1.02399769613271 absolute error = 6.635514360198158e-11 relative error = 6.480009071981526e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 1.999712013823735 y1[1] (numeric) = 1.999712013823469 absolute error = 2.655653474903374e-13 relative error = 1.328017962859255e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.02500000000000002 y2[1] (analytic) = 1.024997395914712 y2[1] (numeric) = 1.024997395996093 absolute error = 8.138023588344367e-11 relative error = 7.939555379145093e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 1.999687516275703 y1[1] (numeric) = 1.999687516275363 absolute error = 3.392841563254478e-13 relative error = 1.696685874987829e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.02600000000000002 y2[1] (analytic) = 1.025997070765676 y2[1] (numeric) = 1.025997070864688 absolute error = 9.901146569291086e-11 relative error = 9.650267872501919e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 1.999662019040238 y1[1] (numeric) = 1.999662019039808 absolute error = 4.292122213200855e-13 relative error = 2.146423831793791e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.02700000000000002 y2[1] (analytic) = 1.026996719619572 y2[1] (numeric) = 1.026996719739146 absolute error = 1.195741283765983e-10 relative error = 1.164308766447588e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 1.999635522142837 y1[1] (numeric) = 1.999635522142299 absolute error = 5.382361223382759e-13 relative error = 2.691671138955836e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.02800000000000002 y2[1] (analytic) = 1.02799634147675 y2[1] (numeric) = 1.02799634162017 absolute error = 1.434197205441023e-10 relative error = 1.395138433450796e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 1.999608025609997 y1[1] (numeric) = 1.999608025609328 absolute error = 6.692424392440444e-13 relative error = 3.346868139518926e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.02900000000000002 y2[1] (analytic) = 1.028995935337589 y2[1] (numeric) = 1.028995935508516 absolute error = 1.709261621130054e-10 relative error = 1.661096572329302e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 1.999579529469216 y1[1] (numeric) = 1.999579529468389 absolute error = 8.262279749260415e-13 relative error = 4.132008568548219e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.03000000000000002 y2[1] (analytic) = 1.029995500202496 y2[1] (numeric) = 1.029995500404996 absolute error = 2.025000167549251e-10 relative error = 1.966028169201845e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 1.999550033748988 y1[1] (numeric) = 1.999550033747975 absolute error = 1.012523398458143e-12 relative error = 5.06375625199909e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.03100000000000002 y2[1] (analytic) = 1.030995035071904 y2[1] (numeric) = 1.03099503531048 absolute error = 2.385762698509097e-10 relative error = 2.314038979191309e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 1.999519538478809 y1[1] (numeric) = 1.999519538477576 absolute error = 1.232791646543774e-12 relative error = 6.165439360905944e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.03200000000000002 y2[1] (analytic) = 1.03199453894628 y2[1] (numeric) = 1.0319945392259 absolute error = 2.796203268928821e-10 relative error = 2.709513629581693e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 1.999488043689175 y1[1] (numeric) = 1.999488043687684 absolute error = 1.49125156667651e-12 relative error = 7.458166961204037e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.03300000000000002 y2[1] (analytic) = 1.03299401082612 y2[1] (numeric) = 1.032994011152248 absolute error = 3.261284575728496e-10 relative error = 3.15711857140424e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 1.999455549411581 y1[1] (numeric) = 1.999455549409788 absolute error = 1.793676318584403e-12 relative error = 8.970823678037068e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.03400000000000002 y2[1] (analytic) = 1.033993449711951 y2[1] (numeric) = 1.03399345009058 absolute error = 3.78628683961324e-10 relative error = 3.661809309012566e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 1.999422055678521 y1[1] (numeric) = 1.999422055676376 absolute error = 2.145617017390578e-12 relative error = 1.073118610098779e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.03500000000000002 y2[1] (analytic) = 1.034992854604336 y2[1] (numeric) = 1.034992855042019 absolute error = 4.376823348195558e-10 relative error = 4.228844024115275e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 1.999387562523488 y1[1] (numeric) = 1.999387562520935 absolute error = 2.55306886742801e-12 relative error = 1.276925452214829e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.03600000000000003 y2[1] (analytic) = 1.035992224503869 y2[1] (numeric) = 1.035992225007754 absolute error = 5.038849337779538e-10 relative error = 4.863790691279189e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 1.999352069980977 y1[1] (numeric) = 1.999352069977953 absolute error = 3.023359340659226e-12 relative error = 1.512169560355617e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.03700000000000003 y2[1] (analytic) = 1.036991558411181 y2[1] (numeric) = 1.036991558989047 absolute error = 5.778664213806906e-10 relative error = 5.572527728828038e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 1.999315578086478 y1[1] (numeric) = 1.999315578082915 absolute error = 3.563371819836902e-12 relative error = 1.782295831080036e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.03800000000000003 y2[1] (analytic) = 1.037990855326937 y2[1] (numeric) = 1.03799085598723 absolute error = 6.602931534871459e-10 relative error = 6.361261759663314e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 1.999278086876485 y1[1] (numeric) = 1.999278086872303 absolute error = 4.181766044553115e-12 relative error = 2.091638012742078e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.03900000000000003 y2[1] (analytic) = 1.038990114251841 y2[1] (numeric) = 1.03899011500371 absolute error = 7.518683453611175e-10 relative error = 7.236530310035961e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 1.999239596388488 y1[1] (numeric) = 1.999239596383601 absolute error = 4.886979709795014e-12 relative error = 2.444419227501828e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.04000000000000003 y2[1] (analytic) = 1.039989334186634 y2[1] (numeric) = 1.039989335039968 absolute error = 8.533334039384499e-10 relative error = 8.205213033322441e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 1.999200106660978 y1[1] (numeric) = 1.999200106655289 absolute error = 5.688782778179302e-12 relative error = 2.84552944911582e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.04100000000000003 y2[1] (analytic) = 1.040988514132096 y2[1] (numeric) = 1.040988515097565 absolute error = 9.654683719162449e-10 relative error = 9.274534337405106e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 1.999159617733445 y1[1] (numeric) = 1.999159617726847 absolute error = 6.59738930153253e-12 relative error = 3.300081315674207e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.04200000000000003 y2[1] (analytic) = 1.041987653089048 y2[1] (numeric) = 1.041987654178142 absolute error = 1.0890937041097e-09 relative error = 1.045207878309309e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.999118129646376 y1[1] (numeric) = 1.999118129638753 absolute error = 7.6234574208911e-12 relative error = 3.813410177136261e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.04300000000000003 y2[1] (analytic) = 1.04298675005835 y2[1] (numeric) = 1.04298675128342 absolute error = 1.225070489496716e-09 relative error = 1.17457914918687e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.999075642441262 y1[1] (numeric) = 1.999075642432483 absolute error = 8.779643678735738e-12 relative error = 4.39185166000726e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.04400000000000003 y2[1] (analytic) = 1.043985804040905 y2[1] (numeric) = 1.043985805415207 absolute error = 1.374302227574731e-09 relative error = 1.316399343990393e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.999032156160589 y1[1] (numeric) = 1.999032156150511 absolute error = 1.007816052833732e-11 relative error = 5.041519966188932e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.04500000000000003 y2[1] (analytic) = 1.04498481403766 y2[1] (numeric) = 1.044984815575395 absolute error = 1.537734606316121e-09 relative error = 1.471537754098599e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.998987670847842 y1[1] (numeric) = 1.998987670836309 absolute error = 1.153299677980613e-11 relative error = 5.769418665255984e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.04600000000000003 y2[1] (analytic) = 1.045983779049605 y2[1] (numeric) = 1.045983780765963 absolute error = 1.716358388748063e-09 relative error = 1.64090344719071e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.998942186547508 y1[1] (numeric) = 1.99894218653435 absolute error = 1.315858533246228e-11 relative error = 6.582774339856849e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.04700000000000003 y2[1] (analytic) = 1.046982698077775 y2[1] (numeric) = 1.046982699988983 absolute error = 1.911208524774111e-09 relative error = 1.825444229673543e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.998895703305071 y1[1] (numeric) = 1.9988957032901 absolute error = 1.497113544246531e-11 relative error = 7.489703148449071e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.04800000000000004 y2[1] (analytic) = 1.04798157012325 y2[1] (numeric) = 1.047981572246616 absolute error = 2.12336637162025e-09 relative error = 2.026148581382521e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.998848221167014 y1[1] (numeric) = 1.998848221150027 absolute error = 1.698685636597475e-11 relative error = 8.498322276844555e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.04900000000000004 y2[1] (analytic) = 1.048980394187159 y2[1] (numeric) = 1.04898039654112 absolute error = 2.353960582013315e-09 relative error = 2.244046309213784e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.998799740180818 y1[1] (numeric) = 1.998799740161594 absolute error = 1.922395576059444e-11 relative error = 9.617749779602919e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.05000000000000004 y2[1] (analytic) = 1.049979169270678 y2[1] (numeric) = 1.049979171874845 absolute error = 2.604166882136383e-09 relative error = 2.480208139696002e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.998750260394966 y1[1] (numeric) = 1.998750260373265 absolute error = 2.170152946234793e-11 relative error = 1.085754928585203e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.05100000000000004 y2[1] (analytic) = 1.050977894375032 y2[1] (numeric) = 1.050977897250243 absolute error = 2.875210736164036e-09 relative error = 2.735748060499207e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.998699781858937 y1[1] (numeric) = 1.998699781834497 absolute error = 2.44395614856785e-11 relative error = 1.222773010108998e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.05200000000000004 y2[1] (analytic) = 1.051976568501496 y2[1] (numeric) = 1.051976571669863 absolute error = 3.168367124217752e-09 relative error = 3.011822904697374e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.998648304623209 y1[1] (numeric) = 1.998648304595749 absolute error = 2.745936811265892e-11 relative error = 1.373896950711178e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.05300000000000004 y2[1] (analytic) = 1.052975190651396 y2[1] (numeric) = 1.052975194136359 absolute error = 3.484962762811961e-09 relative error = 3.309634257057926e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.998595828739259 y1[1] (numeric) = 1.998595828708475 absolute error = 3.078404198220142e-11 relative error = 1.540283510029159e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.05400000000000004 y2[1] (analytic) = 1.05397375982611 y2[1] (numeric) = 1.053973763652485 absolute error = 3.82637543872022e-09 relative error = 3.630427610789396e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.998542354259564 y1[1] (numeric) = 1.998542354225127 absolute error = 3.443756391163788e-11 relative error = 1.723134055089694e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.05500000000000004 y2[1] (analytic) = 1.054972275027068 y2[1] (numeric) = 1.054972279221104 absolute error = 4.194036673510482e-09 relative error = 3.975494686249336e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.998487881237598 y1[1] (numeric) = 1.998487881199153 absolute error = 3.84454690305347e-11 relative error = 1.923727904055474e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.05600000000000004 y2[1] (analytic) = 1.055970735255755 y2[1] (numeric) = 1.055970739845187 absolute error = 4.58943172354509e-09 relative error = 4.346173213250585e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.998432409727834 y1[1] (numeric) = 1.998432409684999 absolute error = 4.283484678069271e-11 relative error = 2.143422343041683e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.05700000000000004 y2[1] (analytic) = 1.056969139513713 y2[1] (numeric) = 1.056969144527813 absolute error = 5.014100690203804e-09 relative error = 4.743847765045134e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.998375939785744 y1[1] (numeric) = 1.99837593973811 absolute error = 4.763434091614727e-11 relative error = 2.383652643518836e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.05800000000000004 y2[1] (analytic) = 1.057967486802535 y2[1] (numeric) = 1.057967492272175 absolute error = 5.469639852151431e-09 relative error = 5.169950797526083e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.998318471467797 y1[1] (numeric) = 1.998318471414923 absolute error = 5.287348336935338e-11 relative error = 2.64589874558468e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.05900000000000005 y2[1] (analytic) = 1.058965776123876 y2[1] (numeric) = 1.058965782081578 absolute error = 5.957702553516242e-09 relative error = 5.625963263254055e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.998260004831461 y1[1] (numeric) = 1.998260004772877 absolute error = 5.858424856342026e-11 relative error = 2.931763054946467e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.06000000000000005 y2[1] (analytic) = 1.059964006479445 y2[1] (numeric) = 1.059964012959445 absolute error = 6.480000092068394e-09 relative error = 6.113415222080051e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.998200539935204 y1[1] (numeric) = 1.998200539870404 absolute error = 6.480016523369159e-11 relative error = 3.242926019617274e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.06100000000000005 y2[1] (analytic) = 1.060962176871012 y2[1] (numeric) = 1.060962183909315 absolute error = 7.03830260739835e-09 relative error = 6.633886448389422e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.99814007683849 y1[1] (numeric) = 1.998140076766934 absolute error = 7.155631642774551e-11 relative error = 3.581146149721585e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.06200000000000005 y2[1] (analytic) = 1.061960286300408 y2[1] (numeric) = 1.061960293934849 absolute error = 7.634440413184507e-09 relative error = 7.189007453170305e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.998078615601783 y1[1] (numeric) = 1.998078615522893 absolute error = 7.88895615499996e-11 relative error = 3.948271150794513e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.06300000000000004 y2[1] (analytic) = 1.062958333769523 y2[1] (numeric) = 1.062958342039828 absolute error = 8.270304663327011e-09 relative error = 7.780459873717145e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.998016156286543 y1[1] (numeric) = 1.998016156199705 absolute error = 8.683853636171079e-11 relative error = 4.346237946499215e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.06400000000000004 y2[1] (analytic) = 1.063956318280309 y2[1] (numeric) = 1.063956327228158 absolute error = 8.947848462170782e-09 relative error = 8.409977278609841e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.99795269895523 y1[1] (numeric) = 1.997952698859786 absolute error = 9.544387502558038e-11 relative error = 4.777083815622358e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.06500000000000004 y2[1] (analytic) = 1.064954238834783 y2[1] (numeric) = 1.064954248503871 absolute error = 9.669088640862356e-09 relative error = 9.079346593748261e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.997888243671301 y1[1] (numeric) = 1.997888243566552 absolute error = 1.047486541949638e-10 relative error = 5.242968645857721e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.06600000000000004 y2[1] (analytic) = 1.065952094435022 y2[1] (numeric) = 1.065952104871127 absolute error = 1.043610486917146e-08 relative error = 9.790407020779689e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 1.997822790499212 y1[1] (numeric) = 1.997822790384414 absolute error = 1.14797504835451e-10 relative error = 5.746130506738571e-09 % Correct digits = 10 h = 0.001 Finished! Maximum Time Reached before Solution Completed! diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * y2 + 1.0; Iterations = 66 Total Elapsed Time = 3 Minutes 2 Seconds Elapsed Time(since restart) = 2 Minutes 58 Seconds Expected Time Remaining = 3 Hours 43 Minutes 20 Seconds Optimized Time Remaining = 3 Hours 38 Minutes 25 Seconds Expected Total Time = 3 Hours 41 Minutes 27 Seconds Time to Timeout Unknown Percent Done = 1.34 %