##############ECHO OF PROBLEM################# ##############temp/arcsin_c_arccos_c_arctan_cpostode.ode################# diff ( y , x , 1 ) = arcsin ( 0.1 ) + arccos ( 0.1 ) + arctan ( 0.1 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-5.0); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(20.0); glob_subiter_method=3; glob_max_iter=1000; glob_upper_ratio_limit=c(1.11); glob_lower_ratio_limit=c(0.99); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return((arcsin(c(0.1)) + arccos(c(0.1)) + arctan(c(0.1))) * c(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -5 y[1] (closed_form) = -8.352324896430293 y[1] (numeric) = -8.352324896430293 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.9 y[1] (closed_form) = -8.185278398501687 y[1] (numeric) = -8.185278398501687 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.800000000000001 y[1] (closed_form) = -8.018231900573083 y[1] (numeric) = -8.018231900573081 absolute error = 1.77635683940025e-15 relative error = 2.215397186595825e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.700000000000001 y[1] (closed_form) = -7.851185402644477 y[1] (numeric) = -7.851185402644475 absolute error = 1.77635683940025e-15 relative error = 2.262533296948928e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.600000000000001 y[1] (closed_form) = -7.684138904715872 y[1] (numeric) = -7.684138904715869 absolute error = 2.664535259100376e-15 relative error = 3.467578205106509e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.500000000000002 y[1] (closed_form) = -7.517092406787267 y[1] (numeric) = -7.517092406787263 absolute error = 3.552713678800501e-15 relative error = 4.726180664737759e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.400000000000002 y[1] (closed_form) = -7.350045908858662 y[1] (numeric) = -7.350045908858657 absolute error = 4.440892098500626e-15 relative error = 6.041992327079522e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.300000000000002 y[1] (closed_form) = -7.182999410930056 y[1] (numeric) = -7.182999410930051 absolute error = 4.440892098500626e-15 relative error = 6.182503776546487e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.200000000000003 y[1] (closed_form) = -7.015952913001451 y[1] (numeric) = -7.015952913001446 absolute error = 5.329070518200751e-15 relative error = 7.595647496899968e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.100000000000003 y[1] (closed_form) = -6.848906415072846 y[1] (numeric) = -6.84890641507284 absolute error = 6.217248937900877e-15 relative error = 9.077725057270693e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.000000000000004 y[1] (closed_form) = -6.681859917144241 y[1] (numeric) = -6.681859917144234 absolute error = 7.105427357601002e-15 relative error = 1.063390649565995e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.900000000000004 y[1] (closed_form) = -6.514813419215635 y[1] (numeric) = -6.514813419215628 absolute error = 7.105427357601002e-15 relative error = 1.090657076477944e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.800000000000004 y[1] (closed_form) = -6.34776692128703 y[1] (numeric) = -6.347766921287022 absolute error = 7.993605777301127e-15 relative error = 1.259278400801836e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.700000000000005 y[1] (closed_form) = -6.180720423358425 y[1] (numeric) = -6.180720423358416 absolute error = 8.881784197001252e-15 relative error = 1.437014391305399e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.600000000000005 y[1] (closed_form) = -6.01367392542982 y[1] (numeric) = -6.01367392542981 absolute error = 9.769962616701378e-15 relative error = 1.624624603503603e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.500000000000005 y[1] (closed_form) = -5.846627427501214 y[1] (numeric) = -5.846627427501204 absolute error = 9.769962616701378e-15 relative error = 1.671042449317992e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.400000000000006 y[1] (closed_form) = -5.679580929572609 y[1] (numeric) = -5.679580929572598 absolute error = 1.06581410364015e-14 relative error = 1.876571734528226e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.300000000000006 y[1] (closed_form) = -5.512534431644004 y[1] (numeric) = -5.512534431643992 absolute error = 1.154631945610163e-14 relative error = 2.094557340054231e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.200000000000006 y[1] (closed_form) = -5.345487933715399 y[1] (numeric) = -5.345487933715386 absolute error = 1.243449787580175e-14 relative error = 2.326167045925612e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.100000000000007 y[1] (closed_form) = -5.178441435786793 y[1] (numeric) = -5.17844143578678 absolute error = 1.243449787580175e-14 relative error = 2.401204692568374e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.000000000000007 y[1] (closed_form) = -5.011394937858188 y[1] (numeric) = -5.011394937858174 absolute error = 1.332267629550188e-14 relative error = 2.658476623914985e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.900000000000007 y[1] (closed_form) = -4.844348439929583 y[1] (numeric) = -4.844348439929568 absolute error = 1.4210854715202e-14 relative error = 2.933491447078603e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.800000000000008 y[1] (closed_form) = -4.677301942000978 y[1] (numeric) = -4.677301942000962 absolute error = 1.509903313490213e-14 relative error = 3.228150186182479e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.700000000000008 y[1] (closed_form) = -4.510255444072372 y[1] (numeric) = -4.510255444072357 absolute error = 1.509903313490213e-14 relative error = 3.347711304189238e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.600000000000009 y[1] (closed_form) = -4.343208946143767 y[1] (numeric) = -4.343208946143751 absolute error = 1.598721155460225e-14 relative error = 3.680967633113052e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.500000000000009 y[1] (closed_form) = -4.176162448215162 y[1] (numeric) = -4.176162448215145 absolute error = 1.687538997430238e-14 relative error = 4.040884468350771e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.400000000000009 y[1] (closed_form) = -4.009115950286557 y[1] (numeric) = -4.009115950286539 absolute error = 1.77635683940025e-14 relative error = 4.430794373191634e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.30000000000001 y[1] (closed_form) = -3.842069452357951 y[1] (numeric) = -3.842069452357933 absolute error = 1.820765760385257e-14 relative error = 4.739023546978876e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.20000000000001 y[1] (closed_form) = -3.675022954429346 y[1] (numeric) = -3.675022954429327 absolute error = 1.865174681370263e-14 relative error = 5.075273554746778e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.10000000000001 y[1] (closed_form) = -3.507976456500741 y[1] (numeric) = -3.507976456500721 absolute error = 1.953992523340276e-14 relative error = 5.57014149772662e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.000000000000011 y[1] (closed_form) = -3.340929958572135 y[1] (numeric) = -3.340929958572115 absolute error = 1.998401444325282e-14 relative error = 5.981572403808697e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.900000000000011 y[1] (closed_form) = -3.173883460643529 y[1] (numeric) = -3.173883460643509 absolute error = 1.998401444325282e-14 relative error = 6.296392004009154e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.80000000000001 y[1] (closed_form) = -3.006836962714923 y[1] (numeric) = -3.006836962714903 absolute error = 1.998401444325282e-14 relative error = 6.646191559787438e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.70000000000001 y[1] (closed_form) = -2.839790464786317 y[1] (numeric) = -2.839790464786297 absolute error = 1.998401444325282e-14 relative error = 7.037144004480814e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.60000000000001 y[1] (closed_form) = -2.672743966857711 y[1] (numeric) = -2.672743966857691 absolute error = 1.953992523340276e-14 relative error = 7.310810715766178e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.50000000000001 y[1] (closed_form) = -2.505697468929105 y[1] (numeric) = -2.505697468929085 absolute error = 1.953992523340276e-14 relative error = 7.798198096817254e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.40000000000001 y[1] (closed_form) = -2.338650971000499 y[1] (numeric) = -2.338650971000479 absolute error = 1.953992523340276e-14 relative error = 8.35521224658991e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.30000000000001 y[1] (closed_form) = -2.171604473071893 y[1] (numeric) = -2.171604473071874 absolute error = 1.953992523340276e-14 relative error = 8.997920880942976e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.20000000000001 y[1] (closed_form) = -2.004557975143287 y[1] (numeric) = -2.004557975143268 absolute error = 1.953992523340276e-14 relative error = 9.74774762102155e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.10000000000001 y[1] (closed_form) = -1.837511477214681 y[1] (numeric) = -1.837511477214662 absolute error = 1.931788062847772e-14 relative error = 1.051306664911828e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.00000000000001 y[1] (closed_form) = -1.670464979286075 y[1] (numeric) = -1.670464979286056 absolute error = 1.931788062847772e-14 relative error = 1.15643733140301e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9000000000000097 y[1] (closed_form) = -1.503418481357469 y[1] (numeric) = -1.50341848135745 absolute error = 1.909583602355269e-14 relative error = 1.27016105364826e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8000000000000096 y[1] (closed_form) = -1.336371983428863 y[1] (numeric) = -1.336371983428844 absolute error = 1.909583602355269e-14 relative error = 1.42893118535429e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7000000000000095 y[1] (closed_form) = -1.169325485500257 y[1] (numeric) = -1.169325485500238 absolute error = 1.887379141862766e-14 relative error = 1.614075093091223e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6000000000000094 y[1] (closed_form) = -1.002278987571651 y[1] (numeric) = -1.002278987571632 absolute error = 1.887379141862766e-14 relative error = 1.883087608606422e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5000000000000093 y[1] (closed_form) = -0.8352324896430449 y[1] (numeric) = -0.8352324896430261 absolute error = 1.876276911616515e-14 relative error = 2.246412747208126e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4000000000000093 y[1] (closed_form) = -0.668185991714439 y[1] (numeric) = -0.6681859917144202 absolute error = 1.887379141862766e-14 relative error = 2.824631412909612e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3000000000000094 y[1] (closed_form) = -0.5011394937858332 y[1] (numeric) = -0.5011394937858142 absolute error = 1.898481372109018e-14 relative error = 3.788329189078744e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2000000000000094 y[1] (closed_form) = -0.3340929958572274 y[1] (numeric) = -0.3340929958572083 absolute error = 1.909583602355269e-14 relative error = 5.715724741416962e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1000000000000094 y[1] (closed_form) = -0.1670464979286216 y[1] (numeric) = -0.1670464979286024 absolute error = 1.915134717478395e-14 relative error = 1.146468044063232e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -9.395262345890387e-15 y[1] (closed_form) = -1.569445672001487e-14 y[1] (numeric) = 3.469446951953614e-15 absolute error = 1.916390367196849e-14 relative error = 122.1061933767295 % Desired digits = 8 Estimated correct digits = -2 Correct digits = 1 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09999999999999061 y[1] (closed_form) = 0.1670464979285902 y[1] (numeric) = 0.1670464979286093 absolute error = 1.917910275039958e-14 relative error = 1.148129591953394e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1999999999999906 y[1] (closed_form) = 0.3340929958571961 y[1] (numeric) = 0.3340929958572152 absolute error = 1.909583602355269e-14 relative error = 5.715724741417498e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2999999999999906 y[1] (closed_form) = 0.5011394937858019 y[1] (numeric) = 0.5011394937858211 absolute error = 1.920685832601521e-14 relative error = 3.832637132810899e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3999999999999906 y[1] (closed_form) = 0.6681859917144077 y[1] (numeric) = 0.6681859917144271 absolute error = 1.931788062847772e-14 relative error = 2.89109332850762e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4999999999999906 y[1] (closed_form) = 0.8352324896430136 y[1] (numeric) = 0.835232489643033 absolute error = 1.942890293094024e-14 relative error = 2.326167045925661e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5999999999999907 y[1] (closed_form) = 1.00227898757162 y[1] (numeric) = 1.002278987571639 absolute error = 1.931788062847772e-14 relative error = 1.927395552338398e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6999999999999907 y[1] (closed_form) = 1.169325485500226 y[1] (numeric) = 1.169325485500245 absolute error = 1.931788062847772e-14 relative error = 1.652053330575766e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7999999999999908 y[1] (closed_form) = 1.336371983428832 y[1] (numeric) = 1.336371983428851 absolute error = 1.909583602355269e-14 relative error = 1.428931185354324e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8999999999999909 y[1] (closed_form) = 1.503418481357438 y[1] (numeric) = 1.503418481357457 absolute error = 1.909583602355269e-14 relative error = 1.270161053648286e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.999999999999991 y[1] (closed_form) = 1.670464979286044 y[1] (numeric) = 1.670464979286063 absolute error = 1.909583602355269e-14 relative error = 1.143144948283456e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.099999999999991 y[1] (closed_form) = 1.837511477214649 y[1] (numeric) = 1.837511477214669 absolute error = 1.909583602355269e-14 relative error = 1.039222680257687e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.199999999999991 y[1] (closed_form) = 2.004557975143256 y[1] (numeric) = 2.004557975143274 absolute error = 1.865174681370263e-14 relative error = 9.304668183702536e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.299999999999991 y[1] (closed_form) = 2.171604473071862 y[1] (numeric) = 2.17160447307188 absolute error = 1.865174681370263e-14 relative error = 8.588924477263874e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.399999999999991 y[1] (closed_form) = 2.338650971000467 y[1] (numeric) = 2.338650971000486 absolute error = 1.865174681370263e-14 relative error = 7.975429871745022e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.499999999999991 y[1] (closed_form) = 2.505697468929073 y[1] (numeric) = 2.505697468929092 absolute error = 1.865174681370263e-14 relative error = 7.443734546962018e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.599999999999991 y[1] (closed_form) = 2.672743966857679 y[1] (numeric) = 2.672743966857698 absolute error = 1.865174681370263e-14 relative error = 6.978501137776889e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.699999999999992 y[1] (closed_form) = 2.839790464786286 y[1] (numeric) = 2.839790464786304 absolute error = 1.820765760385257e-14 relative error = 6.41162009297148e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.799999999999992 y[1] (closed_form) = 3.006836962714892 y[1] (numeric) = 3.00683696271491 absolute error = 1.820765760385257e-14 relative error = 6.055418976695284e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.899999999999992 y[1] (closed_form) = 3.173883460643498 y[1] (numeric) = 3.173883460643516 absolute error = 1.820765760385257e-14 relative error = 5.736712714763952e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.999999999999992 y[1] (closed_form) = 3.340929958572104 y[1] (numeric) = 3.340929958572122 absolute error = 1.820765760385257e-14 relative error = 5.449877079025754e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.099999999999992 y[1] (closed_form) = 3.507976456500709 y[1] (numeric) = 3.507976456500728 absolute error = 1.865174681370263e-14 relative error = 5.316953247830003e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.199999999999991 y[1] (closed_form) = 3.675022954429314 y[1] (numeric) = 3.675022954429334 absolute error = 1.909583602355269e-14 relative error = 5.196113401288412e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.299999999999991 y[1] (closed_form) = 3.84206945235792 y[1] (numeric) = 3.84206945235794 absolute error = 1.998401444325282e-14 relative error = 5.201367307659786e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.399999999999991 y[1] (closed_form) = 4.009115950286525 y[1] (numeric) = 4.009115950286545 absolute error = 2.042810365310288e-14 relative error = 5.09541352917042e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.49999999999999 y[1] (closed_form) = 4.17616244821513 y[1] (numeric) = 4.176162448215151 absolute error = 2.042810365310288e-14 relative error = 4.891596988003601e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.59999999999999 y[1] (closed_form) = 4.343208946143736 y[1] (numeric) = 4.343208946143757 absolute error = 2.131628207280301e-14 relative error = 4.907956844150771e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.69999999999999 y[1] (closed_form) = 4.510255444072341 y[1] (numeric) = 4.510255444072363 absolute error = 2.220446049250313e-14 relative error = 4.923104859101854e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.799999999999989 y[1] (closed_form) = 4.677301942000947 y[1] (numeric) = 4.677301942000969 absolute error = 2.220446049250313e-14 relative error = 4.747279685562502e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.899999999999989 y[1] (closed_form) = 4.844348439929552 y[1] (numeric) = 4.844348439929575 absolute error = 2.309263891220326e-14 relative error = 4.76692360150276e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.999999999999988 y[1] (closed_form) = 5.011394937858157 y[1] (numeric) = 5.011394937858181 absolute error = 2.398081733190338e-14 relative error = 4.785257923047002e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.099999999999988 y[1] (closed_form) = 5.178441435786762 y[1] (numeric) = 5.178441435786787 absolute error = 2.486899575160351e-14 relative error = 4.802409385136776e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.199999999999988 y[1] (closed_form) = 5.345487933715368 y[1] (numeric) = 5.345487933715392 absolute error = 2.486899575160351e-14 relative error = 4.652334091851252e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.299999999999987 y[1] (closed_form) = 5.512534431643973 y[1] (numeric) = 5.512534431643998 absolute error = 2.575717417130363e-14 relative error = 4.67247406627485e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.399999999999987 y[1] (closed_form) = 5.679580929572578 y[1] (numeric) = 5.679580929572604 absolute error = 2.664535259100376e-14 relative error = 4.69142933632059e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.499999999999987 y[1] (closed_form) = 5.846627427501183 y[1] (numeric) = 5.84662742750121 absolute error = 2.753353101070388e-14 relative error = 4.709301448078002e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.599999999999986 y[1] (closed_form) = 6.013673925429789 y[1] (numeric) = 6.013673925429816 absolute error = 2.753353101070388e-14 relative error = 4.578487518964723e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.699999999999986 y[1] (closed_form) = 6.180720423358394 y[1] (numeric) = 6.180720423358422 absolute error = 2.842170943040401e-14 relative error = 4.598446052177299e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.799999999999986 y[1] (closed_form) = 6.347766921286999 y[1] (numeric) = 6.347766921287028 absolute error = 2.930988785010413e-14 relative error = 4.617354136273422e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.899999999999985 y[1] (closed_form) = 6.514813419215604 y[1] (numeric) = 6.514813419215634 absolute error = 3.019806626980426e-14 relative error = 4.635292575031284e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.999999999999985 y[1] (closed_form) = 6.68185991714421 y[1] (numeric) = 6.68185991714424 absolute error = 3.019806626980426e-14 relative error = 4.519410260655501e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.099999999999985 y[1] (closed_form) = 6.848906415072815 y[1] (numeric) = 6.848906415072846 absolute error = 3.108624468950438e-14 relative error = 4.538862528635367e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.199999999999984 y[1] (closed_form) = 7.01595291300142 y[1] (numeric) = 7.015952913001452 absolute error = 3.197442310920451e-14 relative error = 4.557388498140002e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.299999999999984 y[1] (closed_form) = 7.182999410930025 y[1] (numeric) = 7.182999410930058 absolute error = 3.286260152890463e-14 relative error = 4.57505279464442e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.399999999999983 y[1] (closed_form) = 7.350045908858631 y[1] (numeric) = 7.350045908858664 absolute error = 3.286260152890463e-14 relative error = 4.471074322038864e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.499999999999983 y[1] (closed_form) = 7.517092406787236 y[1] (numeric) = 7.51709240678727 absolute error = 3.375077994860476e-14 relative error = 4.48987163150089e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.599999999999983 y[1] (closed_form) = 7.684138904715841 y[1] (numeric) = 7.684138904715875 absolute error = 3.463895836830488e-14 relative error = 4.507851666638479e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.699999999999982 y[1] (closed_form) = 7.851185402644446 y[1] (numeric) = 7.851185402644481 absolute error = 3.552713678800501e-14 relative error = 4.525066593897874e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.799999999999982 y[1] (closed_form) = 8.018231900573051 y[1] (numeric) = 8.018231900573086 absolute error = 3.552713678800501e-14 relative error = 4.430794373191668e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.899999999999982 y[1] (closed_form) = 8.185278398501657 y[1] (numeric) = 8.185278398501692 absolute error = 3.552713678800501e-14 relative error = 4.340369998228573e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.999999999999981 y[1] (closed_form) = 8.352324896430263 y[1] (numeric) = 8.352324896430298 absolute error = 3.552713678800501e-14 relative error = 4.253562598264001e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = arcsin ( 0.1 ) + arccos ( 0.1 ) + arctan ( 0.1 ) ; Iterations = 201 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 101 %