##############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 = 0.005 ; 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(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 = 0.005 y1[1] (analytic) = 1.004995834721974 y1[1] (numeric) = 1.004995834721974 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 x[1] = 0.1 y2[1] (analytic) = 1.004995834721974 y2[1] (numeric) = 1.004995834721974 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 y1[1] (analytic) = 1.004995834721974 y1[1] (numeric) = 1.004995834721974 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) = 1.019933422158758 y2[1] (numeric) = 1.004995834721974 absolute error = 0.01493758743678408 relative error = 1.464564952207142 % Correct digits = 1 h = 0.005 y1[1] (analytic) = 1.019933422158758 y1[1] (numeric) = 1.019933422158774 absolute error = 1.554312234475219e-14 relative error = 1.523934994879775e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.3000000000000002 y2[1] (analytic) = 1.044663510874394 y2[1] (numeric) = 1.004995834721974 absolute error = 0.03966767615241973 relative error = 3.797172557431194 % Correct digits = 1 h = 0.005 y1[1] (analytic) = 1.044663510874394 y1[1] (numeric) = 1.044663510874424 absolute error = 3.019806626980426e-14 relative error = 2.890697909466386e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.4000000000000002 y2[1] (analytic) = 1.078939005997115 y2[1] (numeric) = 1.004995834721974 absolute error = 0.07394317127514083 relative error = 6.853322649764183 % Correct digits = 1 h = 0.005 y1[1] (analytic) = 1.078939005997115 y1[1] (numeric) = 1.07893900599716 absolute error = 4.440892098500626e-14 relative error = 4.115980675289907e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5000000000000003 y2[1] (analytic) = 1.122417438109627 y2[1] (numeric) = 1.004995834721974 absolute error = 0.1174216033876532 relative error = 10.46149136683179 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 1.122417438109627 y1[1] (numeric) = 1.122417438109686 absolute error = 5.839773109528323e-14 relative error = 5.202853155385445e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.6000000000000004 y2[1] (analytic) = 1.174664385090322 y2[1] (numeric) = 1.004995834721974 absolute error = 0.1696685503683477 relative error = 14.44400226327638 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 1.174664385090322 y1[1] (numeric) = 1.174664385090394 absolute error = 7.172040739078511e-14 relative error = 6.105608401949669e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.7000000000000005 y2[1] (analytic) = 1.235157812715512 y2[1] (numeric) = 1.004995834721974 absolute error = 0.2301619779935375 relative error = 18.63421626160654 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 1.235157812715512 y1[1] (numeric) = 1.235157812715596 absolute error = 8.415490526658687e-14 relative error = 6.813291742985548e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.8000000000000006 y2[1] (analytic) = 1.303293290652835 y2[1] (numeric) = 1.004995834721974 absolute error = 0.2982974559308607 relative error = 22.88797602736372 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 1.303293290652835 y1[1] (numeric) = 1.30329329065293 absolute error = 9.50350909079134e-14 relative error = 7.291918986271249e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.9000000000000007 y2[1] (analytic) = 1.378390031729336 y2[1] (numeric) = 1.004995834721974 absolute error = 0.3733941970073618 relative error = 27.08915389781941 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 1.378390031729336 y1[1] (numeric) = 1.378390031729441 absolute error = 1.048050535246148e-13 relative error = 7.603439600700373e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.000000000000001 y2[1] (analytic) = 1.459697694131861 y2[1] (numeric) = 1.004995834721974 absolute error = 0.4547018594098866 relative error = 31.15041294083263 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 1.459697694131861 y1[1] (numeric) = 1.459697694131975 absolute error = 1.139088823265411e-13 relative error = 7.803594044470086e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.104999999999998 y2[1] (analytic) = 1.550865566747637 y2[1] (numeric) = 1.004995834721974 absolute error = 0.5458697320256627 relative error = 35.19774658292409 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 1.550865566747637 y1[1] (numeric) = 1.550865566747761 absolute error = 1.239008895481675e-13 relative error = 7.989144398118494e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.204999999999996 y2[1] (analytic) = 1.642306950998197 y2[1] (numeric) = 1.004995834721974 absolute error = 0.6373111162762226 relative error = 38.80584661039545 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 1.642306950998197 y1[1] (numeric) = 1.642306950998328 absolute error = 1.314504061156185e-13 relative error = 8.004009605860997e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.304999999999994 y2[1] (analytic) = 1.737322285956781 y2[1] (numeric) = 1.004995834721974 absolute error = 0.7323264512348067 relative error = 42.15259639241309 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 1.737322285956781 y1[1] (numeric) = 1.737322285956919 absolute error = 1.383337888682945e-13 relative error = 7.962471326505265e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.404999999999992 y2[1] (analytic) = 1.834962209804377 y2[1] (numeric) = 1.004995834721974 absolute error = 0.8299663750824022 relative error = 45.23070669509233 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 1.834962209804377 y1[1] (numeric) = 1.83496220980452 absolute error = 1.436628593864953e-13 relative error = 7.829199894084522e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.50499999999999 y2[1] (analytic) = 1.934251136697366 y2[1] (numeric) = 1.004995834721974 absolute error = 0.9292553019753922 relative error = 48.04212257370299 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 1.934251136697366 y1[1] (numeric) = 1.934251136697514 absolute error = 1.474376176702208e-13 relative error = 7.622465091165094e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.604999999999988 y2[1] (analytic) = 2.034197004498792 y2[1] (numeric) = 1.004995834721974 absolute error = 1.029201169776818 relative error = 50.59496044388305 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.034197004498792 y1[1] (numeric) = 2.034197004498941 absolute error = 1.49213974509621e-13 relative error = 7.335276484019111e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.704999999999986 y2[1] (analytic) = 2.133801187135292 y2[1] (numeric) = 1.004995834721974 absolute error = 1.128805352413317 relative error = 52.9011493300733 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.133801187135292 y1[1] (numeric) = 2.133801187135442 absolute error = 1.501021529293212e-13 relative error = 7.034495708142282e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.804999999999984 y2[1] (analytic) = 2.232068472538728 y2[1] (numeric) = 1.004995834721974 absolute error = 1.227072637816754 relative error = 54.97468616727048 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.232068472538728 y1[1] (numeric) = 2.232068472538878 absolute error = 1.496580637194711e-13 relative error = 6.704904690905464e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.904999999999981 y2[1] (analytic) = 2.328017006476196 y2[1] (numeric) = 1.004995834721974 absolute error = 1.323021171754221 relative error = 56.8303911901749 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.328017006476196 y1[1] (numeric) = 2.328017006476343 absolute error = 1.478817068800709e-13 relative error = 6.352260592112774e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.004999999999979 y2[1] (analytic) = 2.42068810291296 y2[1] (numeric) = 1.004995834721974 absolute error = 1.415692268190985 relative error = 58.48305143018622 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.42068810291296 y1[1] (numeric) = 2.420688102913104 absolute error = 1.443289932012704e-13 relative error = 5.962312659263727e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.104999999999977 y2[1] (analytic) = 2.509155822886416 y2[1] (numeric) = 1.004995834721974 absolute error = 1.504159988164441 relative error = 59.94685441393297 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.509155822886416 y1[1] (numeric) = 2.509155822886555 absolute error = 1.389999226830696e-13 relative error = 5.539708670750092e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.204999999999975 y2[1] (analytic) = 2.592536226182129 y2[1] (numeric) = 1.004995834721974 absolute error = 1.587540391460155 relative error = 61.23503214448924 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.592536226182129 y1[1] (numeric) = 2.592536226182262 absolute error = 1.323385845353187e-13 relative error = 5.104599241423355e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.304999999999973 y2[1] (analytic) = 2.669996203372267 y2[1] (numeric) = 1.004995834721974 absolute error = 1.665000368650293 relative error = 62.35965304172937 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.669996203372267 y1[1] (numeric) = 2.669996203372391 absolute error = 1.243449787580175e-13 relative error = 4.657121931520612e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.404999999999971 y2[1] (analytic) = 2.740761799969608 y2[1] (numeric) = 1.004995834721974 absolute error = 1.735765965247634 relative error = 63.33151480974675 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.740761799969608 y1[1] (numeric) = 2.740761799969723 absolute error = 1.145750161413162e-13 relative error = 4.180407656826896e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.504999999999969 y2[1] (analytic) = 2.80412594952495 y2[1] (numeric) = 1.004995834721974 absolute error = 1.799130114802975 relative error = 64.1601036183046 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.80412594952495 y1[1] (numeric) = 2.804125949525053 absolute error = 1.030286966852145e-13 relative error = 3.674182206497135e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.604999999999967 y2[1] (analytic) = 2.859455538401337 y2[1] (numeric) = 1.004995834721974 absolute error = 1.854459703679363 relative error = 64.85359463627657 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.859455538401337 y1[1] (numeric) = 2.859455538401428 absolute error = 9.14823772291129e-14 relative error = 3.199293571819579e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.704999999999965 y2[1] (analytic) = 2.906197731636247 y2[1] (numeric) = 1.004995834721974 absolute error = 1.901201896914273 relative error = 65.41887622504812 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.906197731636247 y1[1] (numeric) = 2.906197731636326 absolute error = 7.860379014346108e-14 relative error = 2.70469518600875e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.804999999999962 y2[1] (analytic) = 2.943885496685793 y2[1] (numeric) = 1.004995834721974 absolute error = 1.938889661963819 relative error = 65.8615854504738 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.943885496685793 y1[1] (numeric) = 2.943885496685858 absolute error = 6.483702463810914e-14 relative error = 2.202430247749182e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.90499999999996 y2[1] (analytic) = 2.972142269859517 y2[1] (numeric) = 1.004995834721974 absolute error = 1.967146435137543 relative error = 66.18614644010708 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.972142269859517 y1[1] (numeric) = 2.972142269859568 absolute error = 5.10702591327572e-14 relative error = 1.71829793111388e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.004999999999958 y2[1] (analytic) = 2.990685718820316 y2[1] (numeric) = 1.004995834721974 absolute error = 1.985689884098342 relative error = 66.39580587162473 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.990685718820316 y1[1] (numeric) = 2.990685718820353 absolute error = 3.68594044175552e-14 relative error = 1.232473348356192e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.104999999999956 y2[1] (analytic) = 2.999330563555823 y2[1] (numeric) = 1.004995834721974 absolute error = 1.994334728833848 relative error = 66.49266183149506 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.999330563555823 y1[1] (numeric) = 2.999330563555843 absolute error = 2.087219286295294e-14 relative error = 6.958950479339013e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.204999999999954 y2[1] (analytic) = 2.997990427635044 y2[1] (numeric) = 1.004995834721974 absolute error = 1.99299459291307 relative error = 66.47768366909823 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.997990427635044 y1[1] (numeric) = 2.99799042763505 absolute error = 5.329070518200751e-15 relative error = 1.777547542873435e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.304999999999952 y2[1] (analytic) = 2.986678701253113 y2[1] (numeric) = 1.004995834721974 absolute error = 1.981682866531139 relative error = 66.35072147866757 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.986678701253113 y1[1] (numeric) = 2.986678701253102 absolute error = 1.06581410364015e-14 relative error = 3.568559628435993e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.40499999999995 y2[1] (analytic) = 2.965508407440876 y2[1] (numeric) = 1.004995834721974 absolute error = 1.960512572718902 relative error = 66.11050462037811 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.965508407440876 y1[1] (numeric) = 2.965508407440851 absolute error = 2.531308496145357e-14 relative error = 8.53583314683563e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.504999999999947 y2[1] (analytic) = 2.934691072776137 y2[1] (numeric) = 1.004995834721974 absolute error = 1.929695238054163 relative error = 65.75462936985474 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.934691072776137 y1[1] (numeric) = 2.934691072776097 absolute error = 4.085620730620576e-14 relative error = 1.392180856281983e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.604999999999945 y2[1] (analytic) = 2.894534613880011 y2[1] (numeric) = 1.004995834721974 absolute error = 1.889538779158036 relative error = 65.27953647875654 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.894534613880011 y1[1] (numeric) = 2.894534613879955 absolute error = 5.595524044110789e-14 relative error = 1.933134265273203e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.704999999999943 y2[1] (analytic) = 2.845440260815825 y2[1] (numeric) = 1.004995834721974 absolute error = 1.840444426093851 relative error = 64.68048025602096 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.845440260815825 y1[1] (numeric) = 2.845440260815755 absolute error = 6.972200594645983e-14 relative error = 2.450306439625256e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.804999999999941 y2[1] (analytic) = 2.787898548130962 y2[1] (numeric) = 1.004995834721974 absolute error = 1.782902713408988 relative error = 63.95149187205056 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.787898548130962 y1[1] (numeric) = 2.787898548130879 absolute error = 8.348877145181177e-14 relative error = 2.994684706435374e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.904999999999939 y2[1] (analytic) = 2.722484413597808 y2[1] (numeric) = 1.004995834721974 absolute error = 1.717488578875834 relative error = 63.08534110599899 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.722484413597808 y1[1] (numeric) = 2.722484413597712 absolute error = 9.636735853746359e-14 relative error = 3.539684490245163e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.004999999999937 y2[1] (analytic) = 2.64985145362558 y2[1] (numeric) = 1.004995834721974 absolute error = 1.644855618903606 relative error = 62.07350289968448 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.64985145362558 y1[1] (numeric) = 2.649851453625472 absolute error = 1.079136779935652e-13 relative error = 4.072442545634607e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.104999999999935 y2[1] (analytic) = 2.570725392741056 y2[1] (numeric) = 1.004995834721974 absolute error = 1.565729558019082 relative error = 60.90613810561892 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.570725392741056 y1[1] (numeric) = 2.570725392740937 absolute error = 1.194599974496668e-13 relative error = 4.646937311429117e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.204999999999933 y2[1] (analytic) = 2.485896832388997 y2[1] (numeric) = 1.004995834721974 absolute error = 1.480900997667022 relative error = 59.5721020427001 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.485896832388997 y1[1] (numeric) = 2.485896832388868 absolute error = 1.283417816466681e-13 relative error = 5.162795976666863e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.30499999999993 y2[1] (analytic) = 2.396213351503845 y2[1] (numeric) = 1.004995834721974 absolute error = 1.391217516781871 relative error = 58.05900029347359 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.396213351503845 y1[1] (numeric) = 2.396213351503707 absolute error = 1.385558334732195e-13 relative error = 5.782282841645255e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.404999999999928 y2[1] (analytic) = 2.302571037781187 y2[1] (numeric) = 1.004995834721974 absolute error = 1.297575203059213 relative error = 56.35331904068365 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.302571037781187 y1[1] (numeric) = 2.302571037781042 absolute error = 1.456612608308205e-13 relative error = 6.326026795298495e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.504999999999926 y2[1] (analytic) = 2.205905534265709 y2[1] (numeric) = 1.004995834721974 absolute error = 1.200909699543734 relative error = 54.44066760290746 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.205905534265709 y1[1] (numeric) = 2.205905534265558 absolute error = 1.505462421391712e-13 relative error = 6.824691257202197e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.604999999999924 y2[1] (analytic) = 2.107182690715167 y2[1] (numeric) = 1.004995834721974 absolute error = 1.102186855993192 relative error = 52.30618402712467 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.107182690715167 y1[1] (numeric) = 2.10718269071501 absolute error = 1.56319401867222e-13 relative error = 7.418407647139891e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.704999999999922 y2[1] (analytic) = 2.007388913148886 y2[1] (numeric) = 1.004995834721974 absolute error = 1.002393078426912 relative error = 49.93517060201903 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 2.007388913148886 y1[1] (numeric) = 2.007388913148727 absolute error = 1.585398479164724e-13 relative error = 7.897814263992282e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.80499999999992 y2[1] (analytic) = 1.907521308004872 y2[1] (numeric) = 1.004995834721974 absolute error = 0.9025254732828976 relative error = 47.3140441207901 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 1.907521308004872 y1[1] (numeric) = 1.907521308004712 absolute error = 1.600941601509476e-13 relative error = 8.392784892054201e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.904999999999918 y2[1] (analytic) = 1.808577719381882 y2[1] (numeric) = 1.004995834721974 absolute error = 0.8035818846599074 relative error = 44.43170321342606 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 1.808577719381882 y1[1] (numeric) = 1.808577719381722 absolute error = 1.600941601509476e-13 relative error = 8.85193699088934e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 5.004999999999916 y2[1] (analytic) = 1.711546758911034 y2[1] (numeric) = 1.004995834721974 absolute error = 0.70655092418906 relative error = 41.28142690291445 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 1.711546758911034 y1[1] (numeric) = 1.711546758910876 absolute error = 1.583178033115473e-13 relative error = 9.249984114502164e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y2 , x , 1 ) = diff ( y1, x , 1) ; diff ( y1 , x , 1 ) = sin ( x ) ; Iterations = 981 Total Elapsed Time Unknown Elapsed Time(since restart) Unknown Time to Timeout = 20 Minutes 56 Seconds Percent Done = 100.2 %