##############ECHO OF PROBLEM################# ##############temp/lin_arctanpostode.ode################# diff ( y , x , 1 ) = arctan (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=-1.0 x_end=-0.6 ## ## Trouble further ## $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=100 $glob_max_h=0.001 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.01 $glob_look_poles=true $glob_max_iter=10000000 $glob_max_minutes=3 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(10.0 * (0.1 * x + 0.2) * arctan(0.1 * x + 0.2) - 5.0 * ln(1.0 + expt((0.1 * x + 0.2) , 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 desired_abs_gbl_error 1.0e-10 range 0.4 estimated_steps 400000.00000000006 step_error 2.4999999999999997e-16 est_needed_step_err 2.4999999999999997e-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 9.686664026714664e-185 estimated_step_error 9.686664026714664e-185 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 6.500610408548449e-177 estimated_step_error 6.500610408548449e-177 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 4.362486094492734e-169 estimated_step_error 4.362486094492734e-169 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 2.927615257792038e-161 estimated_step_error 2.927615257792038e-161 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 1.9646898754709763e-153 estimated_step_error 1.9646898754709763e-153 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 1.3184817728382486e-145 estimated_step_error 1.3184817728382486e-145 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 8.848191011791856e-138 estimated_step_error 8.848191011791856e-138 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 5.937933375903845e-130 estimated_step_error 5.937933375903845e-130 best_h 0.000256 opt_iter 9 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.984896951977733e-122 estimated_step_error 3.984896951977733e-122 best_h 0.000512 opt_iter 10 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.674242319674759e-114 estimated_step_error 2.674242319674759e-114 best_h 0.001024 opt_iter 11 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.7946848366986512e-106 estimated_step_error 1.7946848366986512e-106 best_h 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] -1.0 y[1] (analytic) 0.04991699822532158 y[1] (numeric) 0.04991699822532158 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2202099874356918 Order of pole (three term test) -14.927477969090038 Radius of convergence (six term test) for eq 1 10.07515494036883 Order of pole (six term test) -0.9445466369930067 TOP MAIN SOLVE Loop x[1] -0.99 y[1] (analytic) 0.050918634917733505 y[1] (numeric) 0.0509186349210475 absolute error 3.3139949118243806e-12 relative error 6.5084127199769274e-09% Correct digits 11 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.219801563869004 Order of pole (three term test) -15.506655493612248 Radius of convergence (six term test) for eq 1 10.076372541217008 Order of pole (six term test) -0.9448751177395227 TOP MAIN SOLVE Loop x[1] -0.98 y[1] (analytic) 0.05193017062867282 y[1] (numeric) 0.05193017063533453 absolute error 6.66171284802175e-12 relative error 1.2828212900851783e-08% Correct digits 10 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2189533752090175 Order of pole (three term test) -16.080714392266895 Radius of convergence (six term test) for eq 1 10.077602219542886 Order of pole (six term test) -0.9452064642553513 TOP MAIN SOLVE Loop x[1] -0.97 y[1] (analytic) 0.052951603369334195 y[1] (numeric) 0.05295160337937507 absolute error 1.0040877851391627e-11 relative error 1.8962367921811768e-08% Correct digits 10 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2176670561902554 Order of pole (three term test) -16.64832499784001 Radius of convergence (six term test) for eq 1 10.078843907212592 Order of pole (six term test) -0.9455408072480758 TOP MAIN SOLVE Loop x[1] -0.96 y[1] (analytic) 0.05398293113212667 y[1] (numeric) 0.05398293114557818 absolute error 1.3451510738615724e-11 relative error 2.49180814315034e-08% Correct digits 10 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2159452416535596 Order of pole (three term test) -17.208169369977988 Radius of convergence (six term test) for eq 1 10.080097536134542 Order of pole (six term test) -0.9458782770946694 TOP MAIN SOLVE Loop x[1] -0.95 y[1] (analytic) 0.05502415189069715 y[1] (numeric) 0.05502415190759293 absolute error 1.6895783383485963e-11 relative error 3.070612231706657e-08% Correct digits 10 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2137915675974892 Order of pole (three term test) -17.75894466237165 Radius of convergence (six term test) for eq 1 10.0813630384094 Order of pole (six term test) -0.9462190035185571 TOP MAIN SOLVE Loop x[1] -0.94 y[1] (analytic) 0.05607526359996047 y[1] (numeric) 0.05607526362033195 absolute error 2.0371482278846997e-11 relative error 3.632882125026936e-08% Correct digits 10 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.21121066952327633 Order of pole (three term test) -18.299366498478484 Radius of convergence (six term test) for eq 1 10.082640346480126 Order of pole (six term test) -0.9465631152666649 TOP MAIN SOLVE Loop x[1] -0.9299999999999999 y[1] (analytic) 0.057136264196115505 y[1] (numeric) 0.05713626421999518 absolute error 2.387967601436003e-11 relative error 4.179425510284504e-08% Correct digits 10 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.20820817799564514 Order of pole (three term test) -18.82817234401731 Radius of convergence (six term test) for eq 1 10.083929393278757 Order of pole (six term test) -0.9469107397936742 TOP MAIN SOLVE Loop x[1] -0.9199999999999999 y[1] (analytic) 0.05820715159667454 y[1] (numeric) 0.05820715162409379 absolute error 2.741924742810653e-11 relative error 4.7106320573970556e-08% Correct digits 10 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.20479071135313498 Order of pole (three term test) -19.34412486396114 Radius of convergence (six term test) for eq 1 10.085230112370827 Order of pole (six term test) -0.9472620029515575 TOP MAIN SOLVE Loop x[1] -0.9099999999999999 y[1] (analytic) 0.059287923700482026 y[1] (numeric) 0.05928792373147439 absolute error 3.099236145498452e-11 relative error 5.227432421407691e-08% Correct digits 10 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2009658655139751 Order of pole (three term test) -19.846015251317482 Radius of convergence (six term test) for eq 1 10.086542438098993 Order of pole (six term test) -0.9476170286810071 TOP MAIN SOLVE Loop x[1] -0.8999999999999999 y[1] (analytic) 0.06037857838774653 y[1] (numeric) 0.06037857842234334 absolute error 3.459681152673255e-11 relative error 5.7299811374415806e-08% Correct digits 10 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.19674220083695962 Order of pole (three term test) -20.332666514623533 Radius of convergence (six term test) for eq 1 10.087866305722935 Order of pole (six term test) -0.9479759387109326 TOP MAIN SOLVE Loop x[1] -0.8899999999999999 y[1] (analytic) 0.06147911352005771 y[1] (numeric) 0.06147911355829136 absolute error 3.8233652355224024e-11 relative error 6.218966111596616e-08% Correct digits 10 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1921292260111031 Order of pole (three term test) -20.80293671080595 Radius of convergence (six term test) for eq 1 10.089201651555875 Order of pole (six term test) -0.9483388522655449 TOP MAIN SOLVE Loop x[1] -0.8799999999999999 y[1] (analytic) 0.06258952694041534 y[1] (numeric) 0.06258952698231822 absolute error 4.1902883940458935e-11 relative error 6.694871488699715e-08% Correct digits 10 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.18713737896298083 Order of pole (three term test) -21.255722109868508 Radius of convergence (six term test) for eq 1 10.09054841309868 Order of pole (six term test) -0.9487058857767146 TOP MAIN SOLVE Loop x[1] -0.8699999999999999 y[1] (analytic) 0.06370981647325438 y[1] (numeric) 0.06370981651885776 absolute error 4.560338218162485e-11 relative error 7.157983605363126e-08% Correct digits 10 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1817780047864836 Order of pole (three term test) -21.689960277777622 Radius of convergence (six term test) for eq 1 10.0919065291697 Order of pole (six term test) -0.9490771526057404 TOP MAIN SOLVE Loop x[1] -0.8599999999999999 y[1] (analytic) 0.06483997992446676 y[1] (numeric) 0.064839979973803 absolute error 4.933624342395859e-11 relative error 7.608923303404976e-08% Correct digits 10 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.17606333071611832 Order of pole (three term test) -22.104633063924094 Radius of convergence (six term test) for eq 1 10.093275940032221 Order of pole (six term test) -0.9494527627702727 TOP MAIN SOLVE Loop x[1] -0.8499999999999999 y[1] (analytic) 0.06598001508143005 y[1] (numeric) 0.06598001513453149 absolute error 5.310143991188454e-11 relative error 8.048109695996393e-08% Correct digits 10 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1700064381817764 Order of pole (three term test) -22.49876947965059 Radius of convergence (six term test) for eq 1 10.094656587515688 Order of pole (six term test) -0.9498328226849893 TOP MAIN SOLVE Loop x[1] -0.8399999999999999 y[1] (analytic) 0.06712991971303305 y[1] (numeric) 0.06712991976993085 absolute error 5.689780591122684e-11 relative error 8.475774461589341e-08% Correct digits 10 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.16362123200000747 Order of pole (three term test) -22.8714484545511 Radius of convergence (six term test) for eq 1 10.096048415135137 Order of pole (six term test) -0.9502174349060724 TOP MAIN SOLVE Loop x[1] -0.8299999999999998 y[1] (analytic) 0.068289691569697 y[1] (numeric) 0.06828969163042455 absolute error 6.072754799024693e-11 relative error 8.892637614019375e-08% Correct digits 10 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.15692240677401245 Order of pole (three term test) -23.22180145757362 Radius of convergence (six term test) for eq 1 10.09745136820344 Order of pole (six term test) -0.9506066978914198 TOP MAIN SOLVE Loop x[1] -0.8199999999999998 y[1] (analytic) 0.06945932838340939 y[1] (numeric) 0.06945932844799785 absolute error 6.458845958068338e-11 relative error 9.298745191453732e-08% Correct digits 10 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.14992541059175632 Order of pole (three term test) -23.54901497038711 Radius of convergence (six term test) for eq 1 10.098865393942358 Order of pole (six term test) -0.9510007057635459 TOP MAIN SOLVE Loop x[1] -0.8099999999999998 y[1] (analytic) 0.0706388278677423 y[1] (numeric) 0.07063882793622389 absolute error 6.848159539440957e-11 relative error 9.694610947201483e-08% Correct digits 10 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.14264640612849733 Order of pole (three term test) -23.852332801013866 Radius of convergence (six term test) for eq 1 10.100290441585253 Order of pole (six term test) -0.9513995480904782 TOP MAIN SOLVE Loop x[1] -0.7999999999999998 y[1] (analytic) 0.07182818771788424 y[1] (numeric) 0.07182818779029003 absolute error 7.240578969724965e-11 relative error 1.0080414388517502e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1351022292766327 Order of pole (three term test) -24.131058226366505 Radius of convergence (six term test) for eq 1 10.101726462477721 Order of pole (six term test) -0.951803309671357 TOP MAIN SOLVE Loop x[1] -0.7899999999999998 y[1] (analytic) 0.07302740561066216 y[1] (numeric) 0.07302740568702437 absolute error 7.636220822337947e-11 relative error 1.0456650840164917e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.12731034544170763 Order of pole (three term test) -24.384555953071782 Radius of convergence (six term test) for eq 1 10.103173410170413 Order of pole (six term test) -0.9522120703388666 TOP MAIN SOLVE Loop x[1] -0.7799999999999998 y[1] (analytic) 0.07423647920457176 y[1] (numeric) 0.07423647928492252 absolute error 8.035076770607219e-11 relative error 1.0823623179198926e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.11928880365873788 Order of pole (three term test) -24.612253886797845 Radius of convergence (six term test) for eq 1 10.104631240509294 Order of pole (six term test) -0.952625904767384 TOP MAIN SOLVE Loop x[1] -0.7699999999999998 y[1] (analytic) 0.07545540613980296 y[1] (numeric) 0.07545540622417439 absolute error 8.437142651196439e-11 relative error 1.1181627775701309e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.11105618869737342 Order of pole (three term test) -24.81364470122572 Radius of convergence (six term test) for eq 1 10.106099911718141 Order of pole (six term test) -0.9530448822978013 TOP MAIN SOLVE Loop x[1] -0.7599999999999998 y[1] (analytic) 0.07668418403826716 y[1] (numeric) 0.07668418412669138 absolute error 8.842422627441948e-11 relative error 1.1530960051722501e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.102631571337773 Order of pole (three term test) -24.98828719881113 Radius of convergence (six term test) for eq 1 10.107579384476812 Order of pole (six term test) -0.9534690667716355 TOP MAIN SOLVE Loop x[1] -0.7499999999999998 y[1] (analytic) 0.0779228105036256 y[1] (numeric) 0.07792281059613362 absolute error 9.250802901483723e-11 relative error 1.1871752111730238e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09403445701123544 Order of pole (three term test) -25.135807456560183 Radius of convergence (six term test) for eq 1 10.109069621993925 Order of pole (six term test) -0.9538985163773646 TOP MAIN SOLVE Loop x[1] -0.7399999999999998 y[1] (analytic) 0.07917128312131357 y[1] (numeric) 0.07917128321793744 absolute error 9.662387556730323e-11 relative error 1.2204409447204132e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.08528473301047342 Order of pole (three term test) -25.255899751183726 Radius of convergence (six term test) for eq 1 10.110570590072642 Order of pole (six term test) -0.954333283511227 TOP MAIN SOLVE Loop x[1] -0.7299999999999998 y[1] (analytic) 0.08042959945857128 y[1] (numeric) 0.08042959955934303 absolute error 1.0077175205402966e-10 relative error 1.252918735545071e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.07640261448384215 Order of pole (three term test) -25.348327259188526 Radius of convergence (six term test) for eq 1 10.11208225717233 Order of pole (six term test) -0.9547734146476223 TOP MAIN SOLVE Loop x[1] -0.7199999999999998 y[1] (analytic) 0.08169775706447183 y[1] (numeric) 0.08169775716942236 absolute error 1.049505343742041e-10 relative error 1.2846195311259566e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.06740858943571224 Order of pole (three term test) -25.412922528699646 Radius of convergence (six term test) for eq 1 10.113604594462716 Order of pole (six term test) -0.9552189502251167 TOP MAIN SOLVE Loop x[1] -0.7099999999999997 y[1] (analytic) 0.08297575346994582 y[1] (numeric) 0.08297575357910711 absolute error 1.0916129111748774e-10 relative error 1.3155805949629182e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.058323362961438426 Order of pole (three term test) -25.44958772107414 Radius of convergence (six term test) for eq 1 10.11513757587361 Order of pole (six term test) -0.9556699245423825 TOP MAIN SOLVE Loop x[1] -0.6999999999999997 y[1] (analytic) 0.08426358618781293 y[1] (numeric) 0.08426358630121693 absolute error 1.1340399452830496e-10 relative error 1.3458244499058195e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.049167800949951525 Order of pole (three term test) -25.458294621650765 Radius of convergence (six term test) for eq 1 10.116681178136835 Order of pole (six term test) -0.9561263656707837 TOP MAIN SOLVE Loop x[1] -0.6899999999999997 y[1] (analytic) 0.08556125271280927 y[1] (numeric) 0.0855612528304879 absolute error 1.1767863072886797e-10 relative error 1.3753729287234996e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0399628734898532 Order of pole (three term test) -25.43908442027092 Radius of convergence (six term test) for eq 1 10.118235380824146 Order of pole (six term test) -0.9565882953756937 TOP MAIN SOLVE Loop x[1] -0.6799999999999997 y[1] (analytic) 0.08686875052161584 y[1] (numeric) 0.08686875064360107 absolute error 1.2198522747475238e-10 relative error 1.4042475198765335e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.030729598215972476 Order of pole (three term test) -25.39206726349067 Radius of convergence (six term test) for eq 1 10.11980016637826 Order of pole (six term test) -0.9570557290526889 TOP MAIN SOLVE Loop x[1] -0.6699999999999997 y[1] (analytic) 0.08818607707288864 y[1] (numeric) 0.0881860771992112 absolute error 1.263225635206311e-10 relative error 1.432454733372723e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.021488983832662276 Order of pole (three term test) -25.3174215816698 Radius of convergence (six term test) for eq 1 10.121375520137896 Order of pole (six term test) -0.9575286756764818 TOP MAIN SOLVE Loop x[1] -0.6599999999999997 y[1] (analytic) 0.08951322980728404 y[1] (numeric) 0.0895132299379758 absolute error 1.3069174908952874e-10 relative error 1.4600271867175308e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.012261974047692225 Order of pole (three term test) -25.21539319535979 Radius of convergence (six term test) for eq 1 10.1229614303551 Order of pole (six term test) -0.9580071377665256 TOP MAIN SOLVE Loop x[1] -0.6499999999999997 y[1] (analytic) 0.09085020614749255 y[1] (numeric) 0.09085020628258424 absolute error 1.350916878362085e-10 relative error 1.486971725929727e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0030693921464631083 Order of pole (three term test) -25.086294206607228 Radius of convergence (six term test) for eq 1 10.124557888212118 Order of pole (six term test) -0.9584911113536521 TOP MAIN SOLVE Loop x[1] -0.6399999999999997 y[1] (analytic) 0.09219700349826254 y[1] (numeric) 0.09219700363778702 absolute error 1.3952447530662937e-10 relative error 1.513329826486809e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.12616488782225 Order of pole (six term test) -0.9589805859810685 TOP MAIN SOLVE Loop x[1] -0.6299999999999997 y[1] (analytic) 0.09355361924643742 y[1] (numeric) 0.09355361939042539 absolute error 1.4398797432146893e-10 relative error 1.539095713038938e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.127782426238403 Order of pole (six term test) -0.9594755446887469 TOP MAIN SOLVE Loop x[1] -0.6199999999999997 y[1] (analytic) 0.09492005076097768 y[1] (numeric) 0.09492005090946089 absolute error 1.4848321183702495e-10 relative error 1.564297644666531e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.129410503442925 Order of pole (six term test) -0.9599759640379517 TOP MAIN SOLVE Loop x[1] -0.6099999999999997 y[1] (analytic) 0.09629629539299625 y[1] (numeric) 0.09629629554600529 absolute error 1.530090359969094e-10 relative error 1.5889400041036048e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 10.131049122339139 Order of pole (six term test) -0.9604818141323594 Finished! diff ( y , x , 1 ) = arctan (0.1 * x + 0.2 ) ; Iterations 400 Total Elapsed Time 1.0 Seconds Elapsed Time(since restart) 1.0 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.25000000000009%