##############ECHO OF PROBLEM################# ##############temp/mtest5postode.ode################# diff ( y2 , x , 1 ) = diff ( y1, x , 1) ; diff ( y1 , x , 1 ) = 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_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); glob_h = 0.00001 ; glob_max_iter = 20; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_h = 0.00001 ; glob_look_poles = true; glob_max_iter = 100; glob_max_minutes = 1; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y1 (double x) { return(2.0 - cos(x)); } double exact_soln_y2 (double x) { return(2.0 - cos(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y2[1] (analytic) = 1.004995834721974 y2[1] (numeric) = 1.004995834721974 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 y1[1] (analytic) = 1.004995834721974 y1[1] (numeric) = 1.004995834721974 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 x[1] = 0.1 y2[1] (analytic) = 1.004995834721974 y2[1] (numeric) = 1.004995834721974 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 y1[1] (analytic) = 1.004995834721974 y1[1] (numeric) = 1.004995834721974 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10001 y2[1] (analytic) = 1.004996833105891 y2[1] (numeric) = 1.004995834721974 absolute error = 9.983839166505248e-07 relative error = 9.934199628918937e-05 % Correct digits = 6 h = 1e-05 y1[1] (analytic) = 1.004996833105891 y1[1] (numeric) = 1.004996833105891 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10002 y2[1] (analytic) = 1.004997831589308 y2[1] (numeric) = 1.004995834721974 absolute error = 1.996867333486918e-06 relative error = 0.0001986936957196279 % Correct digits = 5 h = 1e-05 y1[1] (analytic) = 1.004997831589308 y1[1] (numeric) = 1.004997831589308 absolute error = 2.220446049250313e-16 relative error = 2.209403821039982e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10003 y2[1] (analytic) = 1.004998830172225 y2[1] (numeric) = 1.004995834721974 absolute error = 2.995450250731224e-06 relative error = 0.0002980550982549799 % Correct digits = 5 h = 1e-05 y1[1] (analytic) = 1.004998830172225 y1[1] (numeric) = 1.004998830172225 absolute error = 2.220446049250313e-16 relative error = 2.209401625740996e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10004 y2[1] (analytic) = 1.004999828854642 y2[1] (numeric) = 1.004995834721974 absolute error = 3.994132668161399e-06 relative error = 0.000397426203814716 % Correct digits = 5 h = 1e-05 y1[1] (analytic) = 1.004999828854642 y1[1] (numeric) = 1.004999828854642 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10005 y2[1] (analytic) = 1.00500082763656 y2[1] (numeric) = 1.004995834721974 absolute error = 4.992914585333352e-06 relative error = 0.0004968070122962077 % Correct digits = 5 h = 1e-05 y1[1] (analytic) = 1.00500082763656 y1[1] (numeric) = 1.00500082763656 absolute error = 2.220446049250313e-16 relative error = 2.209397234499888e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10006 y2[1] (analytic) = 1.005001826517977 y2[1] (numeric) = 1.004995834721974 absolute error = 5.991796002691174e-06 relative error = 0.0005961975236851966 % Correct digits = 5 h = 1e-05 y1[1] (analytic) = 1.005001826517977 y1[1] (numeric) = 1.005001826517977 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10007 y2[1] (analytic) = 1.005002825498894 y2[1] (numeric) = 1.004995834721974 absolute error = 6.990776919790775e-06 relative error = 0.0006955977378790432 % Correct digits = 5 h = 1e-05 y1[1] (analytic) = 1.005002825498894 y1[1] (numeric) = 1.005002825498894 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10008 y2[1] (analytic) = 1.005003824579311 y2[1] (numeric) = 1.004995834721974 absolute error = 7.989857336410111e-06 relative error = 0.0007950076547971967 % Correct digits = 5 h = 1e-05 y1[1] (analytic) = 1.005003824579311 y1[1] (numeric) = 1.005003824579311 absolute error = 2.220446049250313e-16 relative error = 2.209390646030407e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10009 y2[1] (analytic) = 1.005004823759227 y2[1] (numeric) = 1.004995834721974 absolute error = 8.98903725299327e-06 relative error = 0.000894427274425382 % Correct digits = 5 h = 1e-05 y1[1] (analytic) = 1.005004823759227 y1[1] (numeric) = 1.005004823759227 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1001 y2[1] (analytic) = 1.005005823038643 y2[1] (numeric) = 1.004995834721974 absolute error = 9.98831666887412e-06 relative error = 0.0009938565966388496 % Correct digits = 5 h = 1e-05 y1[1] (analytic) = 1.005005823038643 y1[1] (numeric) = 1.005005823038643 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10011 y2[1] (analytic) = 1.005006822417558 y2[1] (numeric) = 1.004995834721974 absolute error = 1.098769558405266e-05 relative error = 0.001093295621379127 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005006822417558 y1[1] (numeric) = 1.005006822417559 absolute error = 2.220446049250313e-16 relative error = 2.209384055631581e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10012 y2[1] (analytic) = 1.005007821895973 y2[1] (numeric) = 1.004995834721974 absolute error = 1.198717399875093e-05 relative error = 0.001192744348609827 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005007821895973 y1[1] (numeric) = 1.005007821895973 absolute error = 2.220446049250313e-16 relative error = 2.209381858403236e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10013 y2[1] (analytic) = 1.005008821473887 y2[1] (numeric) = 1.004995834721974 absolute error = 1.29867519127469e-05 relative error = 0.001292202778250373 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005008821473887 y1[1] (numeric) = 1.005008821473887 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10014 y2[1] (analytic) = 1.0050098211513 y2[1] (numeric) = 1.004995834721974 absolute error = 1.398642932559646e-05 relative error = 0.001391670910198087 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050098211513 y1[1] (numeric) = 1.0050098211513 absolute error = 2.220446049250313e-16 relative error = 2.20937746330345e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1001499999999999 y2[1] (analytic) = 1.005010820928212 y2[1] (numeric) = 1.004995834721974 absolute error = 1.498620623774372e-05 relative error = 0.001491148744438661 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005010820928212 y1[1] (numeric) = 1.005010820928212 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1001599999999999 y2[1] (analytic) = 1.005011820804623 y2[1] (numeric) = 1.004995834721974 absolute error = 1.598608264852253e-05 relative error = 0.001590636280847314 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005011820804623 y1[1] (numeric) = 1.005011820804623 absolute error = 2.220446049250313e-16 relative error = 2.209373067346214e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1001699999999999 y2[1] (analytic) = 1.005012820780533 y2[1] (numeric) = 1.004995834721974 absolute error = 1.698605855837698e-05 relative error = 0.001690133519409726 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005012820780533 y1[1] (numeric) = 1.005012820780533 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1001799999999999 y2[1] (analytic) = 1.005013820855941 y2[1] (numeric) = 1.004995834721974 absolute error = 1.798613396686299e-05 relative error = 0.001789640460023199 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005013820855941 y1[1] (numeric) = 1.005013820855941 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1001899999999999 y2[1] (analytic) = 1.005014821030848 y2[1] (numeric) = 1.004995834721974 absolute error = 1.898630887375852e-05 relative error = 0.001889157102607122 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005014821030848 y1[1] (numeric) = 1.005014821030848 absolute error = 2.220446049250313e-16 relative error = 2.209366471802666e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1001999999999999 y2[1] (analytic) = 1.005015821305254 y2[1] (numeric) = 1.004995834721974 absolute error = 1.998658327950764e-05 relative error = 0.001988683447147158 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005015821305254 y1[1] (numeric) = 1.005015821305254 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002099999999999 y2[1] (analytic) = 1.005016821679158 y2[1] (numeric) = 1.004995834721974 absolute error = 2.098695718344423e-05 relative error = 0.0020882194935185 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005016821679158 y1[1] (numeric) = 1.005016821679158 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002199999999999 y2[1] (analytic) = 1.00501782215256 y2[1] (numeric) = 1.004995834721974 absolute error = 2.198743058579034e-05 relative error = 0.002187765241684707 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.00501782215256 y1[1] (numeric) = 1.00501782215256 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002299999999999 y2[1] (analytic) = 1.005018822725461 y2[1] (numeric) = 1.004995834721974 absolute error = 2.29880034863239e-05 relative error = 0.002287320691565147 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005018822725461 y1[1] (numeric) = 1.005018822725461 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002399999999999 y2[1] (analytic) = 1.005019823397859 y2[1] (numeric) = 1.004995834721974 absolute error = 2.398867588504494e-05 relative error = 0.002386885843101275 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005019823397859 y1[1] (numeric) = 1.005019823397859 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002499999999999 y2[1] (analytic) = 1.005020824169756 y2[1] (numeric) = 1.004995834721974 absolute error = 2.49894477817314e-05 relative error = 0.002486460696212448 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005020824169756 y1[1] (numeric) = 1.005020824169756 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002599999999999 y2[1] (analytic) = 1.00502182504115 y2[1] (numeric) = 1.004995834721974 absolute error = 2.599031917616124e-05 relative error = 0.002586045250818017 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.00502182504115 y1[1] (numeric) = 1.005021825041151 absolute error = 2.220446049250313e-16 relative error = 2.209351074698698e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002699999999999 y2[1] (analytic) = 1.005022826012043 y2[1] (numeric) = 1.004995834721974 absolute error = 2.699129006877854e-05 relative error = 0.002685639506903608 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005022826012043 y1[1] (numeric) = 1.005022826012043 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002799999999999 y2[1] (analytic) = 1.005023827082433 y2[1] (numeric) = 1.004995834721974 absolute error = 2.799236045891718e-05 relative error = 0.002785243464344374 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005023827082433 y1[1] (numeric) = 1.005023827082433 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002899999999999 y2[1] (analytic) = 1.005024828252321 y2[1] (numeric) = 1.004995834721974 absolute error = 2.899353034657715e-05 relative error = 0.002884857123081744 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005024828252321 y1[1] (numeric) = 1.005024828252321 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002999999999999 y2[1] (analytic) = 1.005025829521706 y2[1] (numeric) = 1.004995834721974 absolute error = 2.999479973175845e-05 relative error = 0.002984480483057141 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005025829521706 y1[1] (numeric) = 1.005025829521706 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003099999999999 y2[1] (analytic) = 1.005026830890589 y2[1] (numeric) = 1.004995834721974 absolute error = 3.099616861446108e-05 relative error = 0.00308411354421198 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005026830890589 y1[1] (numeric) = 1.005026830890589 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003199999999999 y2[1] (analytic) = 1.005027832358969 y2[1] (numeric) = 1.004995834721974 absolute error = 3.199763699446301e-05 relative error = 0.003183756306465582 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005027832358969 y1[1] (numeric) = 1.005027832358969 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003299999999999 y2[1] (analytic) = 1.005028833926846 y2[1] (numeric) = 1.004995834721974 absolute error = 3.299920487176422e-05 relative error = 0.003283408769759352 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005028833926846 y1[1] (numeric) = 1.005028833926846 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003399999999999 y2[1] (analytic) = 1.00502983559422 y2[1] (numeric) = 1.004995834721974 absolute error = 3.400087224614268e-05 relative error = 0.003383070934012599 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.00502983559422 y1[1] (numeric) = 1.00502983559422 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003499999999999 y2[1] (analytic) = 1.005030837361092 y2[1] (numeric) = 1.004995834721974 absolute error = 3.500263911737633e-05 relative error = 0.003482742799144623 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005030837361092 y1[1] (numeric) = 1.005030837361092 absolute error = 2.220446049250313e-16 relative error = 2.209331262989438e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003599999999999 y2[1] (analytic) = 1.00503183922746 y2[1] (numeric) = 1.004995834721974 absolute error = 3.600450548568723e-05 relative error = 0.003582424365118909 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.00503183922746 y1[1] (numeric) = 1.00503183922746 absolute error = 2.220446049250313e-16 relative error = 2.209329060616734e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003699999999999 y2[1] (analytic) = 1.005032841193325 y2[1] (numeric) = 1.004995834721974 absolute error = 3.700647135085333e-05 relative error = 0.003682115631854748 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005032841193325 y1[1] (numeric) = 1.005032841193325 absolute error = 2.220446049250313e-16 relative error = 2.209326858029701e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003799999999999 y2[1] (analytic) = 1.005033843258687 y2[1] (numeric) = 1.004995834721974 absolute error = 3.800853671265259e-05 relative error = 0.003781816599271426 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005033843258687 y1[1] (numeric) = 1.005033843258687 absolute error = 2.220446049250313e-16 relative error = 2.209324655228341e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003899999999999 y2[1] (analytic) = 1.005034845423545 y2[1] (numeric) = 1.004995834721974 absolute error = 3.901070157108499e-05 relative error = 0.003881527267310315 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005034845423545 y1[1] (numeric) = 1.005034845423546 absolute error = 2.220446049250313e-16 relative error = 2.209322452212654e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003999999999999 y2[1] (analytic) = 1.0050358476879 y2[1] (numeric) = 1.004995834721974 absolute error = 4.001296592592851e-05 relative error = 0.003981247635890693 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050358476879 y1[1] (numeric) = 1.0050358476879 absolute error = 2.220446049250313e-16 relative error = 2.209320248982643e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004099999999998 y2[1] (analytic) = 1.005036850051751 y2[1] (numeric) = 1.004995834721974 absolute error = 4.101532977718314e-05 relative error = 0.00408097770495392 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005036850051751 y1[1] (numeric) = 1.005036850051752 absolute error = 2.220446049250313e-16 relative error = 2.209318045538308e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004199999999998 y2[1] (analytic) = 1.005037852515099 y2[1] (numeric) = 1.004995834721974 absolute error = 4.201779312484888e-05 relative error = 0.004180717474441355 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005037852515099 y1[1] (numeric) = 1.005037852515099 absolute error = 2.220446049250313e-16 relative error = 2.209315841879651e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004299999999998 y2[1] (analytic) = 1.005038855077943 y2[1] (numeric) = 1.004995834721974 absolute error = 4.302035596892573e-05 relative error = 0.004280466944294347 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005038855077943 y1[1] (numeric) = 1.005038855077943 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004399999999998 y2[1] (analytic) = 1.005039857740283 y2[1] (numeric) = 1.004995834721974 absolute error = 4.402301830874755e-05 relative error = 0.004380226114387967 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005039857740283 y1[1] (numeric) = 1.005039857740283 absolute error = 2.220446049250313e-16 relative error = 2.209311433919379e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004499999999998 y2[1] (analytic) = 1.005040860502119 y2[1] (numeric) = 1.004995834721974 absolute error = 4.502578014475844e-05 relative error = 0.00447999498470774 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005040860502119 y1[1] (numeric) = 1.005040860502119 absolute error = 2.220446049250313e-16 relative error = 2.209309229617766e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004599999999998 y2[1] (analytic) = 1.005041863363451 y2[1] (numeric) = 1.004995834721974 absolute error = 4.602864147673635e-05 relative error = 0.004579773555172907 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005041863363451 y1[1] (numeric) = 1.005041863363451 absolute error = 2.220446049250313e-16 relative error = 2.209307025101837e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004699999999998 y2[1] (analytic) = 1.005042866324279 y2[1] (numeric) = 1.004995834721974 absolute error = 4.703160230445924e-05 relative error = 0.004679561825702707 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005042866324279 y1[1] (numeric) = 1.005042866324279 absolute error = 2.220446049250313e-16 relative error = 2.209304820371595e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004799999999998 y2[1] (analytic) = 1.005043869384602 y2[1] (numeric) = 1.004995834721974 absolute error = 4.80346626279271e-05 relative error = 0.004779359796238464 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005043869384602 y1[1] (numeric) = 1.005043869384602 absolute error = 2.220446049250313e-16 relative error = 2.209302615427039e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004899999999998 y2[1] (analytic) = 1.005044872544421 y2[1] (numeric) = 1.004995834721974 absolute error = 4.90378224469179e-05 relative error = 0.004879167466699405 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005044872544421 y1[1] (numeric) = 1.005044872544421 absolute error = 2.220446049250313e-16 relative error = 2.209300410268173e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004999999999998 y2[1] (analytic) = 1.005045875803736 y2[1] (numeric) = 1.004995834721974 absolute error = 5.004108176165367e-05 relative error = 0.004978984837048934 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005045875803736 y1[1] (numeric) = 1.005045875803736 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005099999999998 y2[1] (analytic) = 1.005046879162546 y2[1] (numeric) = 1.004995834721974 absolute error = 5.104444057146829e-05 relative error = 0.005078811907162083 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005046879162546 y1[1] (numeric) = 1.005046879162546 absolute error = 2.220446049250313e-16 relative error = 2.209295999307512e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005199999999998 y2[1] (analytic) = 1.005047882620851 y2[1] (numeric) = 1.004995834721974 absolute error = 5.204789887680583e-05 relative error = 0.005178648677024339 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005047882620851 y1[1] (numeric) = 1.005047882620851 absolute error = 2.220446049250313e-16 relative error = 2.209293793505721e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005299999999998 y2[1] (analytic) = 1.005048886178652 y2[1] (numeric) = 1.004995834721974 absolute error = 5.305145667744426e-05 relative error = 0.005278495146554905 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005048886178652 y1[1] (numeric) = 1.005048886178652 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005399999999998 y2[1] (analytic) = 1.005049889835947 y2[1] (numeric) = 1.004995834721974 absolute error = 5.405511397293949e-05 relative error = 0.005378351315650891 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005049889835947 y1[1] (numeric) = 1.005049889835947 absolute error = 2.220446049250313e-16 relative error = 2.209289381259226e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005499999999998 y2[1] (analytic) = 1.005050893592738 y2[1] (numeric) = 1.004995834721974 absolute error = 5.505887076351357e-05 relative error = 0.005478217184275672 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005050893592738 y1[1] (numeric) = 1.005050893592738 absolute error = 2.220446049250313e-16 relative error = 2.209287174814525e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005599999999998 y2[1] (analytic) = 1.005051897449023 y2[1] (numeric) = 1.004995834721974 absolute error = 5.606272704916648e-05 relative error = 0.005578092752370531 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005051897449023 y1[1] (numeric) = 1.005051897449024 absolute error = 2.220446049250313e-16 relative error = 2.209284968155522e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005699999999998 y2[1] (analytic) = 1.005052901404804 y2[1] (numeric) = 1.004995834721974 absolute error = 5.706668282945415e-05 relative error = 0.005677978019832559 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005052901404804 y1[1] (numeric) = 1.005052901404804 absolute error = 2.220446049250313e-16 relative error = 2.209282761282221e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005799999999998 y2[1] (analytic) = 1.005053905460079 y2[1] (numeric) = 1.004995834721974 absolute error = 5.807073810459862e-05 relative error = 0.005777872986625115 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005053905460079 y1[1] (numeric) = 1.005053905460079 absolute error = 2.220446049250313e-16 relative error = 2.209280554194623e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005899999999998 y2[1] (analytic) = 1.005054909614848 y2[1] (numeric) = 1.004995834721974 absolute error = 5.907489287415579e-05 relative error = 0.005877777652645281 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005054909614848 y1[1] (numeric) = 1.005054909614849 absolute error = 4.440892098500626e-16 relative error = 4.418556693785457e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005999999999998 y2[1] (analytic) = 1.005055913869113 y2[1] (numeric) = 1.004995834721974 absolute error = 6.007914713834772e-05 relative error = 0.005977692017856408 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005055913869113 y1[1] (numeric) = 1.005055913869113 absolute error = 4.440892098500626e-16 relative error = 4.418552278753079e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1006099999999998 y2[1] (analytic) = 1.005056918222871 y2[1] (numeric) = 1.004995834721974 absolute error = 6.108350089695236e-05 relative error = 0.006077616082177656 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005056918222871 y1[1] (numeric) = 1.005056918222872 absolute error = 4.440892098500626e-16 relative error = 4.418547863292115e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1006199999999998 y2[1] (analytic) = 1.005057922676124 y2[1] (numeric) = 1.004995834721974 absolute error = 6.20879541499697e-05 relative error = 0.006177549845550274 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005057922676124 y1[1] (numeric) = 1.005057922676124 absolute error = 2.220446049250313e-16 relative error = 2.209271723701284e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1006299999999998 y2[1] (analytic) = 1.005058927228871 y2[1] (numeric) = 1.004995834721974 absolute error = 6.309250689695567e-05 relative error = 0.00627749330787132 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005058927228871 y1[1] (numeric) = 1.005058927228872 absolute error = 4.440892098500626e-16 relative error = 4.418539031084443e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1006399999999998 y2[1] (analytic) = 1.005059931881112 y2[1] (numeric) = 1.004995834721974 absolute error = 6.40971591381323e-05 relative error = 0.006377446469104122 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005059931881112 y1[1] (numeric) = 1.005059931881113 absolute error = 4.440892098500626e-16 relative error = 4.41853461433774e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1006499999999998 y2[1] (analytic) = 1.005060936632848 y2[1] (numeric) = 1.004995834721974 absolute error = 6.510191087349959e-05 relative error = 0.006477409329189912 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005060936632848 y1[1] (numeric) = 1.005060936632848 absolute error = 2.220446049250313e-16 relative error = 2.209265098581231e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1006599999999997 y2[1] (analytic) = 1.005061941484077 y2[1] (numeric) = 1.004995834721974 absolute error = 6.610676210261346e-05 relative error = 0.006577381888025732 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005061941484077 y1[1] (numeric) = 1.005061941484077 absolute error = 2.220446049250313e-16 relative error = 2.209262889779308e-14 % Correct digits = 15 h = 1e-05 Finished! Maximum Time Reached before Solution Completed! diff ( y2 , x , 1 ) = diff ( y1, x , 1) ; diff ( y1 , x , 1 ) = sin ( x ) ; Iterations = 66 Total Elapsed Time = 1 Minutes 1 Seconds Elapsed Time(since restart) = 1 Minutes 0 Seconds Expected Time Remaining = 5 Days 3 Hours 54 Minutes 18 Seconds Optimized Time Remaining = 5 Days 1 Hours 52 Minutes 25 Seconds Time to Timeout Unknown Percent Done = 0.01367 %