##############ECHO OF PROBLEM################# ##############temp/tan_sqrt_newpostode.ode################# diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=1.4; x_end=2.1; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=1000000; glob_max_h=0.0001; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=1000000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(tan(sqrt(2.0*x + 1.0))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.7000000000000002 estimated_steps = 700000.0000000002 step_error = 1.428571428571428e-16 est_needed_step_err = 1.428571428571428e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.761030142203954e-162 estimated_step_error = 3.761030142203954e-162 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.523983830929007e-154 estimated_step_error = 2.523983830929007e-154 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.693815840049577e-146 estimated_step_error = 1.693815840049577e-146 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.136699177438331e-138 estimated_step_error = 1.136699177438331e-138 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.628240380191778e-131 estimated_step_error = 7.628240380191778e-131 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.119200403304746e-123 estimated_step_error = 5.119200403304746e-123 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.435403603372848e-115 estimated_step_error = 3.435403603372848e-115 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.305415191690144e-107 estimated_step_error = 2.305415191690144e-107 best_h = 0.0001 START of Soultion TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = -2.514161640922489 y[1] (numeric) = -2.514161640922489 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.0001 NO INFO (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] = 1.410099999999999 y[1] (analytic) = -2.476766516712337 y[1] (numeric) = -2.476761735525513 absolute error = 4.78118682378792e-06 relative error = 0.000193041483382716 % Correct digits = 6 h = 0.0001 NO INFO (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] = 1.420099999999998 y[1] (analytic) = -2.440767761672973 y[1] (numeric) = -2.4407584574392 absolute error = 9.304233772766679e-06 relative error = 0.0003812011088834314 % Correct digits = 6 h = 0.0001 NO INFO (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] = 1.430099999999997 y[1] (analytic) = -2.405746059246014 y[1] (numeric) = -2.405732429560618 absolute error = 1.362968539631026e-05 relative error = 0.0005665471359259734 % Correct digits = 6 h = 0.0001 NO INFO (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] = 1.440099999999995 y[1] (analytic) = -2.371660077125356 y[1] (numeric) = -2.3716423083284 absolute error = 1.776879695603029e-05 relative error = 0.0007492134782471655 % Correct digits = 6 h = 0.0001 NO INFO (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] = 1.450099999999994 y[1] (analytic) = -2.338470787914253 y[1] (numeric) = -2.338449055877926 absolute error = 2.173203632782617e-05 relative error = 0.0009293268250406313 % Correct digits = 6 h = 0.0001 NO INFO (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] = 1.460099999999993 y[1] (analytic) = -2.306141310515878 y[1] (numeric) = -2.306115781366851 absolute error = 2.552914902675951e-05 relative error = 0.001107007142639005 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.470099999999992 y[1] (analytic) = -2.27463676444596 y[1] (numeric) = -2.274607595228883 absolute error = 2.916921707685205e-05 relative error = 0.001282368135993655 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.480099999999991 y[1] (analytic) = -2.243924135855697 y[1] (numeric) = -2.243891475143341 absolute error = 3.266071235641377e-05 relative error = 0.001455517672568683 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.49009999999999 y[1] (analytic) = -2.213972154181212 y[1] (numeric) = -2.213936142636192 absolute error = 3.601154502064219e-05 relative error = 0.001626558172948668 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.500099999999989 y[1] (analytic) = -2.184751178449015 y[1] (numeric) = -2.184711949341523 absolute error = 3.922910749132313e-05 relative error = 0.001795586970190922 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.510099999999988 y[1] (analytic) = -2.156233092366906 y[1] (numeric) = -2.156190772052387 absolute error = 4.232031451989471e-05 relative error = 0.001962696643034985 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.520099999999987 y[1] (analytic) = -2.128391207418326 y[1] (numeric) = -2.128345915778686 absolute error = 4.529163964051008e-05 relative error = 0.002127975321578567 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.530099999999986 y[1] (analytic) = -2.101200173256679 y[1] (numeric) = -2.101152024108219 absolute error = 4.814914845985285e-05 relative error = 0.002291506971714448 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.540099999999984 y[1] (analytic) = -2.074635894766025 y[1] (numeric) = -2.07458499623698 absolute error = 5.089852904482939e-05 relative error = 0.002453371657804546 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.550099999999983 y[1] (analytic) = -2.048675455216503 y[1] (numeric) = -2.048621910096807 absolute error = 5.354511969546394e-05 relative error = 0.002613645785579314 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.560099999999982 y[1] (analytic) = -2.023297044998317 y[1] (numeric) = -2.02324095106393 absolute error = 5.609393438676946e-05 relative error = 0.002772402328438933 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.570099999999981 y[1] (analytic) = -1.998479895467372 y[1] (numeric) = -1.998421345781308 absolute error = 5.854968606411326e-05 relative error = 0.002929711036718766 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.58009999999998 y[1] (analytic) = -1.974204217479846 y[1] (numeric) = -1.974143300671822 absolute error = 6.091680802411403e-05 relative error = 0.003085638632758918 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.590099999999979 y[1] (analytic) = -1.950451144232465 y[1] (numeric) = -1.950387944758918 absolute error = 6.31994735476038e-05 relative error = 0.003240248992367037 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.600099999999978 y[1] (analytic) = -1.927202678060593 y[1] (numeric) = -1.927137276446657 absolute error = 6.540161393564503e-05 relative error = 0.003393603313246784 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.610099999999977 y[1] (analytic) = -1.904441640878047 y[1] (numeric) = -1.904374113942936 absolute error = 6.752693511091756e-05 relative error = 0.003545760272275086 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.620099999999976 y[1] (analytic) = -1.882151627971078 y[1] (numeric) = -1.882082049038168 absolute error = 6.957893290970851e-05 relative error = 0.003696776172316851 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.630099999999975 y[1] (analytic) = -1.860316964884571 y[1] (numeric) = -1.860245403977386 absolute error = 7.156090718485331e-05 relative error = 0.003846705079598816 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.640099999999973 y[1] (analytic) = -1.83892266716168 y[1] (numeric) = -1.838849191186885 absolute error = 7.347597479512302e-05 relative error = 0.003995598950799324 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.650099999999972 y[1] (analytic) = -1.81795440271898 y[1] (numeric) = -1.817879075637346 absolute error = 7.532708163382473e-05 relative error = 0.004143507753613819 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.660099999999971 y[1] (analytic) = -1.797398456657946 y[1] (numeric) = -1.79732133964423 absolute error = 7.711701371571067e-05 relative error = 0.004290479577861706 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.67009999999997 y[1] (analytic) = -1.777241698330704 y[1] (numeric) = -1.777162849923233 absolute error = 7.884840747007793e-05 relative error = 0.004436560741520823 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.680099999999969 y[1] (analytic) = -1.757471550493284 y[1] (numeric) = -1.757391026734049 absolute error = 8.05237592349517e-05 relative error = 0.004581795888095624 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.690099999999968 y[1] (analytic) = -1.738075960393635 y[1] (numeric) = -1.737993814959551 absolute error = 8.214543408424646e-05 relative error = 0.004726228079562321 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.700099999999967 y[1] (analytic) = -1.719043372654231 y[1] (numeric) = -1.718959656980239 absolute error = 8.371567399190205e-05 relative error = 0.004869898882344293 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.710099999999966 y[1] (analytic) = -1.700362703820664 y[1] (numeric) = -1.700277467215229 absolute error = 8.523660543491296e-05 relative error = 0.005012848449533083 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.720099999999965 y[1] (analytic) = -1.682023318457966 y[1] (numeric) = -1.681936608211538 absolute error = 8.671024642814551e-05 relative error = 0.005155115596592271 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.730099999999964 y[1] (analytic) = -1.664015006685972 y[1] (numeric) = -1.66392686817288 absolute error = 8.813851309197318e-05 relative error = 0.005296737874227984 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.740099999999962 y[1] (analytic) = -1.646327963053605 y[1] (numeric) = -1.646238439827868 absolute error = 8.952322573718696e-05 relative error = 0.005437751635533146 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.750099999999961 y[1] (analytic) = -1.62895276665992 y[1] (numeric) = -1.628861900545371 absolute error = 9.086611454978133e-05 relative error = 0.005578192100443611 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.76009999999996 y[1] (analytic) = -1.611880362436847 y[1] (numeric) = -1.61178819361197 absolute error = 9.216882487605993e-05 relative error = 0.005718093415861136 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.770099999999959 y[1] (analytic) = -1.595102043515195 y[1] (numeric) = -1.595008610593041 absolute error = 9.343292215402421e-05 relative error = 0.005857488712641985 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.780099999999958 y[1] (analytic) = -1.578609434601479 y[1] (numeric) = -1.578514774704969 absolute error = 9.465989651014084e-05 relative error = 0.005996410159175174 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.790099999999957 y[1] (analytic) = -1.562394476298554 y[1] (numeric) = -1.562298625131494 absolute error = 9.585116706034569e-05 relative error = 0.00613488901262793 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.800099999999956 y[1] (analytic) = -1.546449410308152 y[1] (numeric) = -1.546352402222235 absolute error = 9.700808591728283e-05 relative error = 0.006272955666745838 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.810099999999955 y[1] (analytic) = -1.530766765457946 y[1] (numeric) = -1.530668633516004 absolute error = 9.813194194219221e-05 relative error = 0.006410639697474417 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.820099999999954 y[1] (analytic) = -1.515339344500045 y[1] (numeric) = -1.515240120535787 absolute error = 9.922396425787738e-05 relative error = 0.006547969906411576 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.830099999999953 y[1] (analytic) = -1.500160211631647 y[1] (numeric) = -1.500059926306127 absolute error = 0.0001002853255203107 relative error = 0.006684974360920789 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.840099999999951 y[1] (analytic) = -1.485222680692207 y[1] (numeric) = -1.485121363547199 absolute error = 0.0001013171450083838 relative error = 0.006821680433883737 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.85009999999995 y[1] (analytic) = -1.470520303994655 y[1] (numeric) = -1.470417983503157 absolute error = 0.0001023204914976095 relative error = 0.006958114840009812 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.860099999999949 y[1] (analytic) = -1.456046861751315 y[1] (numeric) = -1.455943565365347 absolute error = 0.0001032963859677327 relative error = 0.007094303671208022 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.870099999999948 y[1] (analytic) = -1.441796352057864 y[1] (numeric) = -1.441692106253732 absolute error = 0.0001042458041311534 relative error = 0.007230272429415168 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.880099999999947 y[1] (analytic) = -1.42776298140128 y[1] (numeric) = -1.427657811722461 absolute error = 0.0001051696788192391 relative error = 0.00736604605871068 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.890099999999946 y[1] (analytic) = -1.413941155660069 y[1] (numeric) = -1.413835086757847 absolute error = 0.0001060689022216454 relative error = 0.007501648975775757 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.900099999999945 y[1] (analytic) = -1.400325471567198 y[1] (numeric) = -1.400218527239223 absolute error = 0.0001069443279746451 relative error = 0.007637105097785345 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.910099999999944 y[1] (analytic) = -1.386910708608268 y[1] (numeric) = -1.386802911835115 absolute error = 0.0001077967731535345 relative error = 0.007772437871051267 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.920099999999943 y[1] (analytic) = -1.373691821329184 y[1] (numeric) = -1.373583194309065 absolute error = 0.0001086270201187123 relative error = 0.007907670296355467 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.930099999999942 y[1] (analytic) = -1.360663932029412 y[1] (numeric) = -1.360554496211141 absolute error = 0.0001094358182711641 relative error = 0.008042824954428096 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.94009999999994 y[1] (analytic) = -1.347822323818444 y[1] (numeric) = -1.347712099932747 absolute error = 0.0001102238856973692 relative error = 0.008177924029711849 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.950099999999939 y[1] (analytic) = -1.33516243401456 y[1] (numeric) = -1.335051442103834 absolute error = 0.0001109919107258328 relative error = 0.008312989333597627 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.960099999999938 y[1] (analytic) = -1.322679847866373 y[1] (numeric) = -1.322568107312983 absolute error = 0.0001117405533894722 relative error = 0.008448042326321214 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.970099999999937 y[1] (analytic) = -1.310370292578865 y[1] (numeric) = -1.31025782213206 absolute error = 0.0001124704468047355 relative error = 0.008583104137944766 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.980099999999936 y[1] (analytic) = -1.298229631626845 y[1] (numeric) = -1.298116449428367 absolute error = 0.0001131821984781123 relative error = 0.008718195588886748 % Correct digits = 5 h = 0.0001 NO INFO (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] = 1.990099999999935 y[1] (analytic) = -1.286253859339782 y[1] (numeric) = -1.286139982948253 absolute error = 0.0001138763915287111 relative error = 0.008853337208812141 % Correct digits = 5 h = 0.0001 NO INFO (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] = 2.000099999999934 y[1] (analytic) = -1.274439095743054 y[1] (numeric) = -1.274324542157194 absolute error = 0.0001145535858597668 relative error = 0.008988549256092703 % Correct digits = 5 h = 0.0001 NO INFO (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] = 2.010099999999955 y[1] (analytic) = -1.262781581641499 y[1] (numeric) = -1.262666367322276 absolute error = 0.0001152143192231225 relative error = 0.009123851733199547 % Correct digits = 5 h = 0.0001 NO INFO (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] = 2.020099999999976 y[1] (analytic) = -1.251277673932233 y[1] (numeric) = -1.251161814823894 absolute error = 0.0001158591083394445 relative error = 0.009259264410540357 % Correct digits = 5 h = 0.0001 NO INFO (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] = 2.030099999999997 y[1] (analytic) = -1.239923841134096 y[1] (numeric) = -1.239807352684296 absolute error = 0.0001164884497997232 relative error = 0.009394806836940651 % Correct digits = 5 h = 0.0001 NO INFO (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] = 2.040000000000018 y[1] (analytic) = -1.228828016008743 y[1] (numeric) = -1.228710919258855 absolute error = 0.0001170967498882458 relative error = 0.009529140641550336 % Correct digits = 5 h = 0.0001 NO INFO (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] = 2.050000000000039 y[1] (analytic) = -1.217762746753284 y[1] (numeric) = -1.2176450500004 absolute error = 0.0001176967528835338 relative error = 0.009664998637651615 % Correct digits = 5 h = 0.0001 NO INFO (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] = 2.06000000000006 y[1] (analytic) = -1.206837617738705 y[1] (numeric) = -1.206719335056621 absolute error = 0.0001182826820833593 relative error = 0.009801043681832679 % Correct digits = 5 h = 0.0001 NO INFO (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] = 2.070000000000082 y[1] (analytic) = -1.19604950227078 y[1] (numeric) = -1.195930647308146 absolute error = 0.0001188549626343072 relative error = 0.009937294602660933 % Correct digits = 5 h = 0.0001 NO INFO (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] = 2.080000000000103 y[1] (analytic) = -1.185395365828381 y[1] (numeric) = -1.185275951824633 absolute error = 0.0001194140037488189 relative error = 0.01007377008474887 % Correct digits = 4 h = 0.0001 NO INFO (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] = 2.090000000000124 y[1] (analytic) = -1.174872262671408 y[1] (numeric) = -1.174752302471993 absolute error = 0.000119960199414848 relative error = 0.01021048868258105 % Correct digits = 4 h = 0.0001 NO INFO (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 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; Iterations = 7000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 100 %