##############ECHO OF PROBLEM################# ##############temp/arcsin_sqrtpostode.ode################# diff ( y , x , 1 ) = arcsin ( sqrt ( 0.1 * x + 0.2 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.0 x_end=0.5 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=1000000 $glob_display_interval=0.1 $glob_max_minutes=10 $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=30.0 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(10.0 * (0.1 * x + 0.2) * arcsin(sqrt ( 0.1 * x + 0.2)) + 5.0 * sqrt( 0.1 * x + 0.2) * sqrt( 0.8 - 0.1 * x) - 5.0 * arcsin(sqrt( 0.1 * x + 0.2))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 10 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-10 range 0.5 estimated_steps 500000.0 step_error 2.0e-16 est_needed_step_err 2.0e-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 1.2587599705259397e-168 estimated_step_error 1.2587599705259397e-168 best_h 2.0e-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 8.44739325058823e-161 estimated_step_error 8.44739325058823e-161 best_h 4.0e-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 5.668947075830024e-153 estimated_step_error 5.668947075830024e-153 best_h 8.0e-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 3.804362530936719e-145 estimated_step_error 3.804362530936719e-145 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 2.553059843214273e-137 estimated_step_error 2.553059843214273e-137 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 1.7133232387560482e-129 estimated_step_error 1.7133232387560482e-129 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 1.14978341491193e-121 estimated_step_error 1.14978341491193e-121 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 7.71595384942909e-114 estimated_step_error 7.71595384942909e-114 best_h 0.0001 START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y[1] (analytic) 0.609057172997582 y[1] (numeric) 0.609057172997582 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.000220414158401 Order of pole (three term test) 1.4951455387823063 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.010099999999999994 y[1] (analytic) 0.6137463854579579 y[1] (numeric) 0.6137463854578273 absolute error 1.305622276959184e-13 relative error 2.1272993338852344e-11% Correct digits 13 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0103227840412563 Order of pole (three term test) 1.495117840956713 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.020099999999999934 y[1] (analytic) 0.6184017089845004 y[1] (numeric) 0.6184017089842401 absolute error 2.603472992745992e-13 relative error 4.210002907367847e-11% Correct digits 13 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0203251444312373 Order of pole (three term test) 1.495090381916267 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.030099999999999873 y[1] (analytic) 0.6230694858394505 y[1] (numeric) 0.6230694858390594 absolute error 3.9113157157544265e-13 relative error 6.277495214654558e-11% Correct digits 13 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0303275187482144 Order of pole (three term test) 1.4950628875364862 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.04000000000000012 y[1] (analytic) 0.627702829575655 y[1] (numeric) 0.6277028295751359 absolute error 5.191402863147232e-13 relative error 8.270478670068714e-11% Correct digits 13 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0402298830654884 Order of pole (three term test) 1.4950356332249544 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.050000000000000405 y[1] (analytic) 0.6323953205685546 y[1] (numeric) 0.6323953205679056 absolute error 6.490363801958665e-13 relative error 1.0263143307454437e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0502322851721604 Order of pole (three term test) 1.495008068323498 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.06000000000000069 y[1] (analytic) 0.6371001969628831 y[1] (numeric) 0.6371001969621046 absolute error 7.784883848671598e-13 relative error 1.2219245710145555e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.060234701281317 Order of pole (three term test) 1.4949804678853509 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.07000000000000098 y[1] (analytic) 0.6418174364382216 y[1] (numeric) 0.6418174364373137 absolute error 9.07940389538453e-13 relative error 1.414639643598787e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0702371314182972 Order of pole (three term test) 1.4949528318446268 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.08000000000000126 y[1] (analytic) 0.6465470168695733 y[1] (numeric) 0.6465470168685357 absolute error 1.0376144388146713e-12 relative error 1.6048553496365251e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.080239575608559 Order of pole (three term test) 1.4949251601342524 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.09000000000000155 y[1] (analytic) 0.6512889163250826 y[1] (numeric) 0.6512889163239156 absolute error 1.166955421183502e-12 relative error 1.7917630592703517e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.090242033877562 Order of pole (three term test) 1.494897452687838 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.10000000000000184 y[1] (analytic) 0.6560431130637951 y[1] (numeric) 0.6560431130624991 absolute error 1.2960743589474077e-12 relative error 1.975593269921842e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.100244506250882 Order of pole (three term test) 1.4948697094384233 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.11000000000000212 y[1] (analytic) 0.6608095855334555 y[1] (numeric) 0.6608095855320296 absolute error 1.4258594305260885e-12 relative error 2.1577462884032273e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.110246992754026 Order of pole (three term test) 1.494841930319592 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.12000000000000241 y[1] (analytic) 0.6655883123683375 y[1] (numeric) 0.6655883123667825 absolute error 1.5549783682899943e-12 relative error 2.33624650462532e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.120249493412748 Order of pole (three term test) 1.4948141152634908 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.130000000000002 y[1] (analytic) 0.67037927238712 y[1] (numeric) 0.6703792723854353 absolute error 1.684763439868675e-12 relative error 2.513149659101907e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.130252008252709 Order of pole (three term test) 1.4947862642032475 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1400000000000009 y[1] (analytic) 0.6751824445907855 y[1] (numeric) 0.6751824445889727 absolute error 1.8127721546079556e-12 relative error 2.6848626902712796e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1402545372996804 Order of pole (three term test) 1.4947583770711694 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1500999999999998 y[1] (analytic) 0.6800460232926793 y[1] (numeric) 0.6800460232907366 absolute error 1.942668248489099e-12 relative error 2.8566717280148115e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.150357106084187 Order of pole (three term test) 1.494730174384878 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1600999999999987 y[1] (analytic) 0.684873679191655 y[1] (numeric) 0.6848736791895836 absolute error 2.0713430970431546e-12 relative error 3.024416268249535e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1603596637653983 Order of pole (three term test) 1.4947022145440576 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1700999999999976 y[1] (analytic) 0.689713485148133 y[1] (numeric) 0.6897134851459331 absolute error 2.1999069232947477e-12 relative error 3.1895953474394707e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.17036223573152 Order of pole (three term test) 1.494674218427569 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.18009999999999649 y[1] (analytic) 0.6945654208738086 y[1] (numeric) 0.6945654208714801 absolute error 2.328470749546341e-12 relative error 3.3524138685409545e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1803648220085003 Order of pole (three term test) 1.4946461859675015 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19009999999999538 y[1] (analytic) 0.699429466252703 y[1] (numeric) 0.6994294662502457 absolute error 2.457256620402859e-12 relative error 3.513230052442565e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1903674226224434 Order of pole (three term test) 1.4946181170951836 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.20009999999999428 y[1] (analytic) 0.7043056013392688 y[1] (numeric) 0.7043056013366836 absolute error 2.585154312839677e-12 relative error 3.670500856338342e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.200370037599539 Order of pole (three term test) 1.4945900117415016 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.21009999999999318 y[1] (analytic) 0.7091938063565295 y[1] (numeric) 0.7091938063538155 absolute error 2.7140512059986577e-12 relative error 3.82695277605715e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2103726669658026 Order of pole (three term test) 1.4945618698392114 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.22009999999999208 y[1] (analytic) 0.7140940616942388 y[1] (numeric) 0.7140940616913962 absolute error 2.842615032250251e-12 relative error 3.9807291290253064e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.220375310747562 Order of pole (three term test) 1.4945336913184668 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.23009999999999098 y[1] (analytic) 0.7190063479070807 y[1] (numeric) 0.7190063479041098 absolute error 2.970956813896919e-12 relative error 4.1320314104943955e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2303779689710743 Order of pole (three term test) 1.4945054761108554 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.24009999999998988 y[1] (analytic) 0.7239306457128931 y[1] (numeric) 0.7239306457097944 absolute error 3.0987434840312744e-12 relative error 4.2804424738502076e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2403806416627687 Order of pole (three term test) 1.4944772241462358 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2500999999999888 y[1] (analytic) 0.728866935990919 y[1] (numeric) 0.7288669359876923 absolute error 3.226752198770555e-12 relative error 4.4270799503117497e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.250383328848959 Order of pole (three term test) 1.4944489353562156 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2600999999999877 y[1] (analytic) 0.7338151997800888 y[1] (numeric) 0.7338151997767333 absolute error 3.355538069627073e-12 relative error 4.5727290340029306e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.260386030556104 Order of pole (three term test) 1.4944206096711643 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2700999999999866 y[1] (analytic) 0.7387754182773252 y[1] (numeric) 0.7387754182738416 absolute error 3.4835467843663537e-12 relative error 4.715298720265057e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.270388746810852 Order of pole (three term test) 1.4943922470207207 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.28009999999998547 y[1] (analytic) 0.7437475728358804 y[1] (numeric) 0.7437475728322683 absolute error 3.612110610617947e-12 relative error 4.856635157604764e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2803914776396663 Order of pole (three term test) 1.4943638473356342 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.29009999999998437 y[1] (analytic) 0.7487316449636947 y[1] (numeric) 0.7487316449599548 absolute error 3.739897280752302e-12 relative error 4.994976913168464e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2903942230692493 Order of pole (three term test) 1.4943354105455287 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.30009999999998327 y[1] (analytic) 0.7537276163217848 y[1] (numeric) 0.7537276163179164 absolute error 3.868350084701433e-12 relative error 5.132291826560776e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.300396983126333 Order of pole (three term test) 1.494306936580409 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.31009999999998217 y[1] (analytic) 0.758735468722652 y[1] (numeric) 0.758735468718655 absolute error 3.996913910953026e-12 relative error 5.267862220388774e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3103997578376285 Order of pole (three term test) 1.4942784253695234 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.32009999999998107 y[1] (analytic) 0.76375518412872 y[1] (numeric) 0.7637551841245958 absolute error 4.1242564918775315e-12 relative error 5.39997184645289e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3204025472299503 Order of pole (three term test) 1.49424987684299 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.33009999999997997 y[1] (analytic) 0.768786744650797 y[1] (numeric) 0.7687867446465451 absolute error 4.2519321397094245e-12 relative error 5.53070428086109e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.330405351330243 Order of pole (three term test) 1.4942212909294 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.34009999999997886 y[1] (analytic) 0.7738301325465557 y[1] (numeric) 0.7738301325421753 absolute error 4.380495965961018e-12 relative error 5.660797869870329e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.34040817016549 Order of pole (three term test) 1.4941926675575183 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.35009999999997776 y[1] (analytic) 0.7788853302190413 y[1] (numeric) 0.7788853302145338 absolute error 4.5075054799781356e-12 relative error 5.78712334806783e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3504110037626456 Order of pole (three term test) 1.4941640066567314 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.36009999999997666 y[1] (analytic) 0.7839523202152039 y[1] (numeric) 0.7839523202105687 absolute error 4.6351811278100286e-12 relative error 5.912580406085945e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.360413852148776 Order of pole (three term test) 1.4941353081555995 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.37009999999997556 y[1] (analytic) 0.7890310852244493 y[1] (numeric) 0.7890310852196859 absolute error 4.763411887154234e-12 relative error 6.037039574681933e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3704167153510456 Order of pole (three term test) 1.494106571982644 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.38009999999997446 y[1] (analytic) 0.7941216080772131 y[1] (numeric) 0.7941216080723213 absolute error 4.891753668800902e-12 relative error 6.159955375909218e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3804195933965526 Order of pole (three term test) 1.4940777980667788 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.39009999999997336 y[1] (analytic) 0.7992238717435547 y[1] (numeric) 0.799223871738535 absolute error 5.01965136123772e-12 relative error 6.28065744618845e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.390422486312727 Order of pole (three term test) 1.4940489863347626 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.40009999999997226 y[1] (analytic) 0.8043378593317785 y[1] (numeric) 0.8043378593266308 absolute error 5.147660075977001e-12 relative error 6.39987290944322e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.4004253941267844 Order of pole (three term test) 1.4940201367154144 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.41009999999997115 y[1] (analytic) 0.8094635540870674 y[1] (numeric) 0.8094635540817914 absolute error 5.276001857623669e-12 relative error 6.517899207425184e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.4104283168660707 Order of pole (three term test) 1.4939912491367946 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.42009999999997005 y[1] (analytic) 0.814600939390143 y[1] (numeric) 0.8146009393847401 absolute error 5.402900349338324e-12 relative error 6.632573187778602e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.4204312545580335 Order of pole (three term test) 1.493962323526337 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.43009999999996895 y[1] (analytic) 0.8197499987559462 y[1] (numeric) 0.8197499987504147 absolute error 5.53157519789238e-12 relative error 6.747880703003484e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.4304342072302383 Order of pole (three term test) 1.493933359811236 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.44009999999996785 y[1] (analytic) 0.8249107158323259 y[1] (numeric) 0.8249107158266676 absolute error 5.65825164500211e-12 relative error 6.859229170387241e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.440437174910188 Order of pole (three term test) 1.493904357918914 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.45009999999996675 y[1] (analytic) 0.830083074398769 y[1] (numeric) 0.8300830743929823 absolute error 5.786704448951241e-12 relative error 6.971235322612213e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.450440157625582 Order of pole (three term test) 1.493875317775837 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.46009999999996565 y[1] (analytic) 0.8352670583651229 y[1] (numeric) 0.835267058359209 absolute error 5.913936007573284e-12 relative error 7.08029359992802e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.460443155404056 Order of pole (three term test) 1.4938462393096603 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.47009999999996455 y[1] (analytic) 0.8404626517703595 y[1] (numeric) 0.8404626517643176 absolute error 6.0419447223125644e-12 relative error 7.188831900603492e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.470446168273307 Order of pole (three term test) 1.4938171224471113 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.48009999999996344 y[1] (analytic) 0.8456698387813435 y[1] (numeric) 0.8456698387751738 absolute error 6.16973139244692e-12 relative error 7.295673925580508e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.480449196261214 Order of pole (three term test) 1.493787967114404 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.49009999999996234 y[1] (analytic) 0.8508886036916219 y[1] (numeric) 0.8508886036853246 absolute error 6.2972960179763504e-12 relative error 7.40084658632778e-10% Correct digits 12 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.4904522393956356 Order of pole (three term test) 1.4937587732377604 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = arcsin ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations 5001 Total Elapsed Time 5 Seconds Elapsed Time(since restart) 5 Seconds Time to Timeout 29 Minutes 55.0 Seconds Percent Done 100.03999999999225%