##############ECHO OF PROBLEM################# ##############temp/arccos_sqrtpostode.ode################# diff ( y , x , 1 ) = arccos ( 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=10.0 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(10.0 * (0.1 * x + 0.2) * arccos(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) 2.532535480592211 y[1] (numeric) 2.532535480592211 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) 2.5437113110324643 y[1] (numeric) 2.5437113110325953 absolute error 1.3100631690576847e-13 relative error 5.1502038119488665e-12% Correct digits 14 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) 2.5547639507738698 y[1] (numeric) 2.554763950774132 absolute error 2.62456723021387e-13 relative error 1.0273227902009719e-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) 2.565804137186869 y[1] (numeric) 2.5658041371872606 absolute error 3.9168668308775523e-13 relative error 1.526565014885345e-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) 2.5767216770859345 y[1] (numeric) 2.576721677086455 absolute error 5.204725539442734e-13 relative error 2.019902104960308e-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 2.040229883065497 Order of pole (three term test) 1.495035633224884 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.050000000000000405 y[1] (analytic) 2.587737149360984 y[1] (numeric) 2.5877371493616357 absolute error 6.514788708500419e-13 relative error 2.517561998176353e-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 2.0502322851721604 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) 2.5987402362346046 y[1] (numeric) 2.5987402362353866 absolute error 7.820410985459603e-13 relative error 3.009308462776887e-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 2.060234701281317 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) 2.609730960027216 y[1] (numeric) 2.6097309600281284 absolute error 9.126033262418787e-13 relative error 3.496924932953095e-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 2.0702371314182972 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) 2.620709342863814 y[1] (numeric) 2.6207093428648562 absolute error 1.042277375518097e-12 relative error 3.977081160702602e-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 2.0802395756085486 Order of pole (three term test) 1.4949251601343332 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.09000000000000155 y[1] (analytic) 2.6316754066762535 y[1] (numeric) 2.6316754066774246 absolute error 1.1710632463746151e-12 relative error 4.449877228034142e-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 2.090242033877562 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) 2.6426291732054903 y[1] (numeric) 2.6426291732067893 absolute error 1.2989609388114332e-12 relative error 4.9154113334630407e-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 2.100244506250892 Order of pole (three term test) 1.494869709438363 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.11000000000000212 y[1] (analytic) 2.6535706640037793 y[1] (numeric) 2.653570664005207 absolute error 1.4277468096679513e-12 relative error 5.3804740496856724e-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 2.110246992754026 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) 2.664499900436847 y[1] (numeric) 2.664499900438403 absolute error 1.5560885913146194e-12 relative error 5.840077498443506e-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 2.120249493412748 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) 2.6754169036860134 y[1] (numeric) 2.6754169036877 absolute error 1.6866508190105378e-12 relative error 6.304254176935121e-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 2.1302520082527154 Order of pole (three term test) 1.4947862642032526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1400000000000009 y[1] (analytic) 2.686321694750295 y[1] (numeric) 2.686321694752112 absolute error 1.8167689574966062e-12 relative error 6.76303571924018e-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 2.1402545372996635 Order of pole (three term test) 1.4947583770713087 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1500999999999998 y[1] (analytic) 2.697323158949027 y[1] (numeric) 2.697323158950977 absolute error 1.949995720451625e-12 relative error 7.22937373663233e-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 2.150357106084187 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) 2.708203466317999 y[1] (numeric) 2.708203466320079 absolute error 2.0801138589376933e-12 relative error 7.680788702946904e-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 2.160359663765413 Order of pole (three term test) 1.4947022145439557 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1700999999999976 y[1] (analytic) 2.719071623629468 y[1] (numeric) 2.719071623631681 absolute error 2.212896532682862e-12 relative error 8.13842678306887e-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 2.1703622357315013 Order of pole (three term test) 1.4946742184276927 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.18009999999999649 y[1] (analytic) 2.72992765117174 y[1] (numeric) 2.7299276511740826 absolute error 2.3425705819590803e-12 relative error 8.581072033002786e-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 2.1803648220085003 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) 2.740771569060793 y[1] (numeric) 2.7407715690632637 absolute error 2.4709123636057484e-12 relative error 9.015389649756475e-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 2.190367422622459 Order of pole (three term test) 1.494618117095092 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.20009999999999428 y[1] (analytic) 2.751603397242174 y[1] (numeric) 2.7516033972447755 absolute error 2.601474591301667e-12 relative error 9.454395186126839e-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 2.200370037599547 Order of pole (three term test) 1.4945900117413842 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.21009999999999318 y[1] (analytic) 2.7624231554928604 y[1] (numeric) 2.7624231554955916 absolute error 2.731148640577885e-12 relative error 9.886785937003213e-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 2.2103726669658026 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) 2.7732308634230987 y[1] (numeric) 2.773230863425959 absolute error 2.8603786006442533e-12 relative error 1.0314246240262828e-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) 2.784026540478204 y[1] (numeric) 2.7840265404811952 absolute error 2.9913849175500218e-12 relative error 1.0744814656243186e-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) 2.794810205940339 y[1] (numeric) 2.79481020594346 absolute error 3.12105896682624e-12 relative error 1.1167337804164529e-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) 2.80558187893026 y[1] (numeric) 2.80558187893351 absolute error 3.2502889268926083e-12 relative error 1.1585079556230634e-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) 2.816341578409037 y[1] (numeric) 2.8163415784124193 absolute error 3.382183422218077e-12 relative error 1.2009137840903112e-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) 2.8270893231797483 y[1] (numeric) 2.827089323183259 absolute error 3.510525203864745e-12 relative error 1.2417454146501134e-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) 2.83782513188914 y[1] (numeric) 2.837825131892781 absolute error 3.641087431560663e-12 relative error 1.2830556015045197e-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) 2.8485490230292734 y[1] (numeric) 2.8485490230330472 absolute error 3.773870105305832e-12 relative error 1.324839444501654e-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) 2.8592610149391304 y[1] (numeric) 2.859261014943036 absolute error 3.905764600631301e-12 relative error 1.366004915334548e-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) 2.8699611258062108 y[1] (numeric) 2.8699611258102444 absolute error 4.033662293068119e-12 relative error 1.405476282169156e-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) 2.88064937366809 y[1] (numeric) 2.8806493736722527 absolute error 4.162892253134487e-12 relative error 1.4451228570847019e-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) 2.8913257764139595 y[1] (numeric) 2.8913257764182525 absolute error 4.293010391620555e-12 relative error 1.4847895822189468e-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) 2.9019903517861483 y[1] (numeric) 2.901990351790572 absolute error 4.423572619316474e-12 relative error 1.5243236823974295e-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 2.3404081701655057 Order of pole (three term test) 1.4941926675574204 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.35009999999997776 y[1] (analytic) 2.9126431173816103 y[1] (numeric) 2.9126431173861618 absolute error 4.551470311753292e-12 relative error 1.5626598001628651e-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) 2.923284090653395 y[1] (numeric) 2.923284090658077 absolute error 4.68203253944921e-12 relative error 1.60163446119351e-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) 2.9339132889120965 y[1] (numeric) 2.933913288916909 absolute error 4.8125947671451286e-12 relative error 1.640332993252726e-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 2.3704167153510403 Order of pole (three term test) 1.49410657198264 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.38009999999997446 y[1] (analytic) 2.94453072932728 y[1] (numeric) 2.944530729332223 absolute error 4.942712905631197e-12 relative error 1.6786080228004377e-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 2.3804195933965953 Order of pole (three term test) 1.4940777980663587 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.39009999999997336 y[1] (analytic) 2.9551364289288857 y[1] (numeric) 2.95513642893396 absolute error 5.0741633117468155e-12 relative error 1.717065669819511e-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) 2.9657304046086095 y[1] (numeric) 2.965730404613811 absolute error 5.2016169149737834e-12 relative error 1.7539075388952107e-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 2.4004253941267772 Order of pole (three term test) 1.4940201367154105 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.41009999999997115 y[1] (analytic) 2.9763126731212677 y[1] (numeric) 2.9763126731265963 absolute error 5.328626428990901e-12 relative error 1.790344971854975e-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) 2.986883251086139 y[1] (numeric) 2.986883251091597 absolute error 5.4578563890572696e-12 relative error 1.8272747644463824e-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) 2.997442154988283 y[1] (numeric) 2.9974421549938706 absolute error 5.587530438333488e-12 relative error 1.86409950531817e-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 2.4304342072302396 Order of pole (three term test) 1.4939333598111686 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.44009999999996785 y[1] (analytic) 3.0079894011798505 y[1] (numeric) 3.0079894011855677 absolute error 5.717204487609706e-12 relative error 1.9006730826136541e-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) 3.018525005881355 y[1] (numeric) 3.0185250058872035 absolute error 5.848654893725325e-12 relative error 1.9375870275481195e-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) 3.0290489851829476 y[1] (numeric) 3.0290489851889255 absolute error 5.977884853791693e-12 relative error 1.9735187126498855e-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) 3.039561355045658 y[1] (numeric) 3.039561355051767 absolute error 6.108891170697461e-12 relative error 2.009793669917776e-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) 3.0500621313026217 y[1] (numeric) 3.0500621313088594 absolute error 6.2376770415539795e-12 relative error 2.0450983530915779e-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) 3.060551329660291 y[1] (numeric) 3.060551329666658 absolute error 6.367351090830198e-12 relative error 2.080458847111363e-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 ) = arccos ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations 5001 Total Elapsed Time 5 Seconds Elapsed Time(since restart) 5 Seconds Time to Timeout 9 Minutes 55.0 Seconds Percent Done 100.03999999999225%