##############ECHO OF PROBLEM################# ##############temp/expt_sin_sinpostode.ode################# diff ( y , x , 1 ) = expt ( sin ( 0.1 * x ) , sin ( 0.2 * x ) ) ; ! /* 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=0; /* 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(0.0)); } /* 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 y[1] (numeric) = 0 absolute error = 0 relative error = -1 % Desired digits = 8 Estimated correct digits = -16 Correct digits = -16 h = 0.05 SETTING H FOR POLE NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09997 Order of pole (three term test) = 2.013 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1999667308992541 y[1] (closed_form) = 0 y[1] (numeric) = 0.08834376929164249 absolute error = 0.08834376929164249 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1998 Order of pole (three term test) = 2.023 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2999334617985082 y[1] (closed_form) = 0 y[1] (numeric) = 0.1716316828905853 absolute error = 0.1716316828905853 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2997 Order of pole (three term test) = 2.032 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3999001926977623 y[1] (closed_form) = 0 y[1] (numeric) = 0.2508253976222287 absolute error = 0.2508253976222287 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3995 Order of pole (three term test) = 2.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4998669235970165 y[1] (closed_form) = 0 y[1] (numeric) = 0.3265757408880771 absolute error = 0.3265757408880771 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4992 Order of pole (three term test) = 2.048 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.59983365449627 y[1] (closed_form) = 0 y[1] (numeric) = 0.3993667047260413 absolute error = 0.3993667047260413 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.599 Order of pole (three term test) = 2.056 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6998003853955236 y[1] (closed_form) = 0 y[1] (numeric) = 0.469577784049566 absolute error = 0.469577784049566 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6986 Order of pole (three term test) = 2.063 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7997671162947771 y[1] (closed_form) = 0 y[1] (numeric) = 0.5375170530160087 absolute error = 0.5375170530160087 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7983 Order of pole (three term test) = 2.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8997338471940307 y[1] (closed_form) = 0 y[1] (numeric) = 0.6034409058390552 absolute error = 0.6034409058390552 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8979 Order of pole (three term test) = 2.076 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9997005780932843 y[1] (closed_form) = 0 y[1] (numeric) = 0.6675667959347448 absolute error = 0.6675667959347448 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9975 Order of pole (three term test) = 2.083 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.099667308992539 y[1] (closed_form) = 0 y[1] (numeric) = 0.7300819308818675 absolute error = 0.7300819308818675 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.097 Order of pole (three term test) = 2.089 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.199634039891794 y[1] (closed_form) = 0 y[1] (numeric) = 0.7911494638630939 absolute error = 0.7911494638630939 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.197 Order of pole (three term test) = 2.095 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.299600770791048 y[1] (closed_form) = 0 y[1] (numeric) = 0.8509130512531369 absolute error = 0.8509130512531369 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.296 Order of pole (three term test) = 2.101 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.399567501690303 y[1] (closed_form) = 0 y[1] (numeric) = 0.9095002984978641 absolute error = 0.9095002984978641 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.396 Order of pole (three term test) = 2.107 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.499534232589558 y[1] (closed_form) = 0 y[1] (numeric) = 0.9670254235352994 absolute error = 0.9670254235352994 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.495 Order of pole (three term test) = 2.112 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.599500963488812 y[1] (closed_form) = 0 y[1] (numeric) = 1.023591353846944 absolute error = 1.023591353846944 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.594 Order of pole (three term test) = 2.118 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.699467694388067 y[1] (closed_form) = 0 y[1] (numeric) = 1.07929140375653 absolute error = 1.07929140375653 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.694 Order of pole (three term test) = 2.123 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.799434425287322 y[1] (closed_form) = 0 y[1] (numeric) = 1.134210634294927 absolute error = 1.134210634294927 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.793 Order of pole (three term test) = 2.128 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.899401156186576 y[1] (closed_form) = 0 y[1] (numeric) = 1.188426968778173 absolute error = 1.188426968778173 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.893 Order of pole (three term test) = 2.133 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.999367887085831 y[1] (closed_form) = 0 y[1] (numeric) = 1.242012117495444 absolute error = 1.242012117495444 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.992 Order of pole (three term test) = 2.138 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.099334617985083 y[1] (closed_form) = 0 y[1] (numeric) = 1.295032351205962 absolute error = 1.295032351205962 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.091 Order of pole (three term test) = 2.143 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.199301348884336 y[1] (closed_form) = 0 y[1] (numeric) = 1.347549153440665 absolute error = 1.347549153440665 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.191 Order of pole (three term test) = 2.148 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.299268079783588 y[1] (closed_form) = 0 y[1] (numeric) = 1.399619774600838 absolute error = 1.399619774600838 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.29 Order of pole (three term test) = 2.152 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.399234810682841 y[1] (closed_form) = 0 y[1] (numeric) = 1.451297705705738 absolute error = 1.451297705705738 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.389 Order of pole (three term test) = 2.157 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.499201541582093 y[1] (closed_form) = 0 y[1] (numeric) = 1.502633085811699 absolute error = 1.502633085811699 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.488 Order of pole (three term test) = 2.161 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.599168272481346 y[1] (closed_form) = 0 y[1] (numeric) = 1.553673054233318 absolute error = 1.553673054233318 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.588 Order of pole (three term test) = 2.165 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.699135003380598 y[1] (closed_form) = 0 y[1] (numeric) = 1.60446205648648 absolute error = 1.60446205648648 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.687 Order of pole (three term test) = 2.17 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.799101734279851 y[1] (closed_form) = 0 y[1] (numeric) = 1.655042111163865 absolute error = 1.655042111163865 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.786 Order of pole (three term test) = 2.174 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.899068465179103 y[1] (closed_form) = 0 y[1] (numeric) = 1.705453043618766 absolute error = 1.705453043618766 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.885 Order of pole (three term test) = 2.178 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.999035196078355 y[1] (closed_form) = 0 y[1] (numeric) = 1.755732691280653 absolute error = 1.755732691280653 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.984 Order of pole (three term test) = 2.182 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.099001926977608 y[1] (closed_form) = 0 y[1] (numeric) = 1.805917084589161 absolute error = 1.805917084589161 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.083 Order of pole (three term test) = 2.186 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.208965330966786 y[1] (closed_form) = 0 y[1] (numeric) = 1.861050889319023 absolute error = 1.861050889319023 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.192 Order of pole (three term test) = 2.19 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.308932061866038 y[1] (closed_form) = 0 y[1] (numeric) = 1.91114537314418 absolute error = 1.91114537314418 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.292 Order of pole (three term test) = 2.193 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.408898792765291 y[1] (closed_form) = 0 y[1] (numeric) = 1.961246439853098 absolute error = 1.961246439853098 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.391 Order of pole (three term test) = 2.197 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.508865523664543 y[1] (closed_form) = 0 y[1] (numeric) = 2.011384197826408 absolute error = 2.011384197826408 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.49 Order of pole (three term test) = 2.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.608832254563795 y[1] (closed_form) = 0 y[1] (numeric) = 2.061587595794913 absolute error = 2.061587595794913 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.589 Order of pole (three term test) = 2.204 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.708798985463048 y[1] (closed_form) = 0 y[1] (numeric) = 2.111884510275162 absolute error = 2.111884510275162 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.688 Order of pole (three term test) = 2.207 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.8087657163623 y[1] (closed_form) = 0 y[1] (numeric) = 2.16230182347004 absolute error = 2.16230182347004 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.787 Order of pole (three term test) = 2.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.908732447261553 y[1] (closed_form) = 0 y[1] (numeric) = 2.212865492675912 absolute error = 2.212865492675912 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.886 Order of pole (three term test) = 2.213 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.008699178160805 y[1] (closed_form) = 0 y[1] (numeric) = 2.263600612097192 absolute error = 2.263600612097192 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.985 Order of pole (three term test) = 2.216 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.108665909060058 y[1] (closed_form) = 0 y[1] (numeric) = 2.314531467850602 absolute error = 2.314531467850602 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.084 Order of pole (three term test) = 2.219 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.20863263995931 y[1] (closed_form) = 0 y[1] (numeric) = 2.365681586841095 absolute error = 2.365681586841095 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.183 Order of pole (three term test) = 2.222 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.308599370858563 y[1] (closed_form) = 0 y[1] (numeric) = 2.417073780106218 absolute error = 2.417073780106218 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.282 Order of pole (three term test) = 2.225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.408566101757815 y[1] (closed_form) = 0 y[1] (numeric) = 2.468730181153198 absolute error = 2.468730181153198 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.381 Order of pole (three term test) = 2.227 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.508532832657068 y[1] (closed_form) = 0 y[1] (numeric) = 2.520672279751138 absolute error = 2.520672279751138 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.48 Order of pole (three term test) = 2.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.60849956355632 y[1] (closed_form) = 0 y[1] (numeric) = 2.572920951587727 absolute error = 2.572920951587727 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.58 Order of pole (three term test) = 2.232 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.708466294455572 y[1] (closed_form) = 0 y[1] (numeric) = 2.625496484154442 absolute error = 2.625496484154442 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.679 Order of pole (three term test) = 2.235 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.808433025354825 y[1] (closed_form) = 0 y[1] (numeric) = 2.678418599185204 absolute error = 2.678418599185204 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.778 Order of pole (three term test) = 2.237 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.908399756254077 y[1] (closed_form) = 0 y[1] (numeric) = 2.731706471939872 absolute error = 2.731706471939872 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.0099966730899254 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.877 Order of pole (three term test) = 2.239 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = expt ( sin ( 0.1 * x ) , sin ( 0.2 * x ) ) ; Iterations = 491 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 100.4 %