##############ECHO OF PROBLEM################# ##############temp/mult_sin_linpostode.ode################# diff ( y , x , 1 ) = sin ( x ) * ( 0.2 * x + 0.3 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.1); 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(c(0.2) * sin(c(x)) - c(0.2) * cos(c(x)) * c(x) - c(0.3) * cos(c(x))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = -0.2984346495596026 y[1] (numeric) = -0.2984346495596026 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] = 0.2 y[1] (closed_form) = -0.2934887703070099 y[1] (numeric) = -0.2934887703070099 absolute error = 5.551115123125783e-17 relative error = 1.891423347243892e-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] = 0.3 y[1] (closed_form) = -0.2848170947529503 y[1] (numeric) = -0.2848170947529503 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] = 0.4 y[1] (closed_form) = -0.2721195092593662 y[1] (numeric) = -0.2721195092593662 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] = 0.4999999999999999 y[1] (closed_form) = -0.2551479170353085 y[1] (numeric) = -0.2551479170353085 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] = 0.6 y[1] (closed_form) = -0.2337124635830578 y[1] (numeric) = -0.2337124635830578 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] = 0.7000000000000001 y[1] (closed_form) = -0.2076870249576367 y[1] (numeric) = -0.2076870249576367 absolute error = 2.775557561562891e-17 relative error = 1.336413558877374e-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] = 0.8000000000000002 y[1] (closed_form) = -0.1770138681197915 y[1] (numeric) = -0.1770138681197915 absolute error = 5.551115123125783e-17 relative error = 3.13597752655693e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4664 Order of pole (three term test) = 22.38 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 0.9355595931132374 y[1] (closed_form) = -0.1280504167254812 y[1] (numeric) = -0.1280504167254812 absolute error = 2.775557561562891e-17 relative error = 2.167550588697595e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.04360889105658637 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.416 Order of pole (three term test) = 22.25 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.016529188492399 y[1] (closed_form) = -0.09484280141079326 y[1] (numeric) = -0.09484280141079329 absolute error = 2.775557561562891e-17 relative error = 2.926482052698022e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.03936711229639342 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3698 Order of pole (three term test) = 22.18 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.120030628489818 y[1] (closed_form) = -0.04826306721434781 y[1] (numeric) = -0.04826306721434773 absolute error = 7.632783294297951e-17 relative error = 1.58149569325939e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.03201573268331002 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2956 Order of pole (three term test) = 22.11 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.201634286593477 y[1] (closed_form) = -0.008442321985503168 y[1] (numeric) = -0.008442321985503163 absolute error = 5.204170427930421e-18 relative error = 6.164382781024964e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = 0.02488083368532419 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2272 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.307100664721442 y[1] (closed_form) = 0.04675236779421994 y[1] (numeric) = 0.04675236779421994 absolute error = 6.938893903907228e-18 relative error = 1.484180209748669e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.02068741627455316 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] = 1.410537746094208 y[1] (closed_form) = 0.1045482838495757 y[1] (numeric) = 0.1045482838495757 absolute error = 4.163336342344337e-17 relative error = 3.982213948470502e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.02068741627455316 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] = 1.513974827466974 y[1] (closed_form) = 0.1654439331998777 y[1] (numeric) = 0.1654439331998776 absolute error = 8.326672684688674e-17 relative error = 5.032927181819943e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 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] = 1.61741190883974 y[1] (closed_form) = 0.2288362072921264 y[1] (numeric) = 0.2288362072921263 absolute error = 1.110223024625157e-16 relative error = 4.851605599317919e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 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] = 1.700161573937953 y[1] (closed_form) = 0.2808959853523132 y[1] (numeric) = 0.280895985352313 absolute error = 1.665334536937735e-16 relative error = 5.928651970048602e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 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] = 1.803598655310719 y[1] (closed_form) = 0.3470361908496419 y[1] (numeric) = 0.3470361908496418 absolute error = 1.110223024625157e-16 relative error = 3.199156324033581e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 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] = 1.907035736683484 y[1] (closed_form) = 0.4136235057120553 y[1] (numeric) = 0.413623505712055 absolute error = 2.220446049250313e-16 relative error = 5.368278201278243e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 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] = 2.01047281805625 y[1] (closed_form) = 0.4798221497903417 y[1] (numeric) = 0.4798221497903415 absolute error = 2.220446049250313e-16 relative error = 4.627643909770604e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 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] = 2.113909899429016 y[1] (closed_form) = 0.5447573879057492 y[1] (numeric) = 0.544757387905749 absolute error = 2.220446049250313e-16 relative error = 4.076027417978739e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 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] = 2.217346980801782 y[1] (closed_form) = 0.607526666662897 y[1] (numeric) = 0.6075266666628969 absolute error = 1.110223024625157e-16 relative error = 1.827447395393418e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 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] = 2.300096645899995 y[1] (closed_form) = 0.6555655896465848 y[1] (numeric) = 0.6555655896465847 absolute error = 1.110223024625157e-16 relative error = 1.693534624390028e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 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] = 2.403533727272761 y[1] (closed_form) = 0.7121187646113802 y[1] (numeric) = 0.71211876461138 absolute error = 2.220446049250313e-16 relative error = 3.118083892175011e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 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] = 2.506970808645526 y[1] (closed_form) = 0.7639340803852992 y[1] (numeric) = 0.7639340803852991 absolute error = 1.110223024625157e-16 relative error = 1.453296891879994e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3709 Order of pole (three term test) = 22.81 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.610407890018292 y[1] (closed_form) = 0.810115966584775 y[1] (numeric) = 0.8101159665847749 absolute error = 1.110223024625157e-16 relative error = 1.370449504045143e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 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] = 2.713844971391058 y[1] (closed_form) = 0.8498019976946128 y[1] (numeric) = 0.8498019976946127 absolute error = 1.110223024625157e-16 relative error = 1.306449064178512e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 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] = 2.817282052763824 y[1] (closed_form) = 0.8821760540137974 y[1] (numeric) = 0.8821760540137973 absolute error = 1.110223024625157e-16 relative error = 1.258505056415635e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 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] = 2.900031717862037 y[1] (closed_form) = 0.9022997286286576 y[1] (numeric) = 0.9022997286286577 absolute error = 1.110223024625157e-16 relative error = 1.230437059215907e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 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] = 3.003468799234803 y[1] (closed_form) = 0.9196526195325092 y[1] (numeric) = 0.9196526195325091 absolute error = 1.110223024625157e-16 relative error = 1.207219988335945e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 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] = 3.106905880607568 y[1] (closed_form) = 0.9277629051187004 y[1] (numeric) = 0.9277629051187003 absolute error = 1.110223024625157e-16 relative error = 1.196666754512147e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 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] = 3.210342961980334 y[1] (closed_form) = 0.9261038437974384 y[1] (numeric) = 0.9261038437974383 absolute error = 1.110223024625157e-16 relative error = 1.198810513595049e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 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] = 3.3137800433531 y[1] (closed_form) = 0.9142515415801229 y[1] (numeric) = 0.9142515415801229 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 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] = 3.417217124725866 y[1] (closed_form) = 0.891894204253378 y[1] (numeric) = 0.891894204253378 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 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] = 3.499966789824079 y[1] (closed_form) = 0.8663116907704695 y[1] (numeric) = 0.8663116907704693 absolute error = 2.220446049250313e-16 relative error = 2.563102948865345e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02068741627455316 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] = 3.603403871196845 y[1] (closed_form) = 0.8246472766805804 y[1] (numeric) = 0.8246472766805802 absolute error = 1.110223024625157e-16 relative error = 1.346300480241798e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.02068741627455316 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] = 3.70684095256961 y[1] (closed_form) = 0.7722641306215212 y[1] (numeric) = 0.7722641306215211 absolute error = 1.110223024625157e-16 relative error = 1.437620861312883e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.02068741627455316 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] = 3.810278033942376 y[1] (closed_form) = 0.7093374908245813 y[1] (numeric) = 0.7093374908245814 absolute error = 1.110223024625157e-16 relative error = 1.565154864907195e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.02068741627455316 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] = 3.913715115315142 y[1] (closed_form) = 0.6361797626826573 y[1] (numeric) = 0.6361797626826575 absolute error = 2.220446049250313e-16 relative error = 3.490280860062391e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.02068741627455316 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] = 4.017152196687908 y[1] (closed_form) = 0.5532410303132652 y[1] (numeric) = 0.5532410303132657 absolute error = 4.440892098500626e-16 relative error = 8.027047625130102e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.02068741627455316 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] = 4.099901861786121 y[1] (closed_form) = 0.4802373347805465 y[1] (numeric) = 0.4802373347805468 absolute error = 2.775557561562891e-16 relative error = 5.779553900846202e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.02068741627455316 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] = 4.203338943158887 y[1] (closed_form) = 0.3812605378365192 y[1] (numeric) = 0.3812605378365195 absolute error = 3.33066907387547e-16 relative error = 8.735939714022089e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.02068741627455316 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] = 4.306776024531652 y[1] (closed_form) = 0.2744777822461547 y[1] (numeric) = 0.2744777822461552 absolute error = 4.996003610813204e-16 relative error = 1.820185069235488e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.02068741627455316 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] = 4.410213105904418 y[1] (closed_form) = 0.1608355110709083 y[1] (numeric) = 0.1608355110709088 absolute error = 5.273559366969494e-16 relative error = 3.278852618962062e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.02068741627455316 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] = 4.513650187277184 y[1] (closed_form) = 0.04139545516060347 y[1] (numeric) = 0.04139545516060407 absolute error = 6.036837696399289e-16 relative error = 1.458333450611413e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.02068741627455316 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] = 4.61708726864995 y[1] (closed_form) = -0.08267508015035885 y[1] (numeric) = -0.08267508015035818 absolute error = 6.661338147750939e-16 relative error = 8.057250305214281e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.02068741627455316 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] = 4.699836933748163 y[1] (closed_form) = -0.1844205250480334 y[1] (numeric) = -0.1844205250480327 absolute error = 7.216449660063518e-16 relative error = 3.913040404902844e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.02068741627455316 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] = 4.803274015120929 y[1] (closed_form) = -0.3135915473410665 y[1] (numeric) = -0.3135915473410657 absolute error = 7.771561172376096e-16 relative error = 2.478243191907095e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.02068741627455316 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] = 4.906711096493694 y[1] (closed_form) = -0.4436648047912112 y[1] (numeric) = -0.4436648047912103 absolute error = 8.881784197001252e-16 relative error = 2.001913178842533e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.02068741627455316 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 ) = sin ( x ) * ( 0.2 * x + 0.3 ) ; Iterations = 209 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 100.6 %