##############ECHO OF PROBLEM################# ##############temp/tan_sqrt_newpostode.ode################# diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=-0.4 x_end=0.1 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=1000000 $glob_max_h=0.001 # ELIMINATED in preodein.rb #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(tan(sqrt(2.0*x + 1.0))) 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 0.5 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 9.61683216743226e-134 estimated_step_error 9.61683216743226e-134 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 6.453716339796431e-126 estimated_step_error 6.453716339796431e-126 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 4.330974811693662e-118 estimated_step_error 4.330974811693662e-118 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 2.9064130897081194e-110 estimated_step_error 2.9064130897081194e-110 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 1.9503871175179774e-102 estimated_step_error 1.9503871175179774e-102 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 1.3087837441828608e-94 estimated_step_error 1.3087837441828608e-94 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 8.78177199837587e-87 estimated_step_error 8.78177199837587e-87 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 5.891567125938798e-79 estimated_step_error 5.891567125938798e-79 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 3.951376463442679e-71 estimated_step_error 3.951376463442679e-71 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 2.6485255022602716e-63 estimated_step_error 2.6485255022602716e-63 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 1.773118278595071e-55 estimated_step_error 1.773118278595071e-55 best_h 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] -0.4 y[1] (analytic) 0.47962308588780483 y[1] (numeric) 0.47962308588780483 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.1069528493387683 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.39 y[1] (analytic) 0.5067607579474308 y[1] (numeric) 0.5067607579474308 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.11764555034472796 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.38 y[1] (analytic) 0.5332570683952551 y[1] (numeric) 0.5332570683952553 absolute error 2.220446049250313e-16 relative error 4.16393177109187e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.12833779014855815 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.37 y[1] (analytic) 0.5592299963915907 y[1] (numeric) 0.5592299963915907 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.13902957084230214 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.36 y[1] (analytic) 0.5847761286389005 y[1] (numeric) 0.5847761286389004 absolute error 1.1102230246251565e-16 relative error 1.898543682364845e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.14972089450061457 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.35 y[1] (analytic) 0.6099760485882879 y[1] (numeric) 0.6099760485882878 absolute error 1.1102230246251565e-16 relative error 1.8201092111643183e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.16041176318098985 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.33999999999999997 y[1] (analytic) 0.6348981238362741 y[1] (numeric) 0.6348981238362739 absolute error 2.220446049250313e-16 relative error 3.497326525133844e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.17110217892398621 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.32999999999999996 y[1] (analytic) 0.6596012382901228 y[1] (numeric) 0.6596012382901225 absolute error 3.3306690738754696e-16 relative error 5.0495191344842335e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.18179214375344466 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.31999999999999995 y[1] (analytic) 0.6841368083416924 y[1] (numeric) 0.6841368083416922 absolute error 2.220446049250313e-16 relative error 3.245616990894766e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.19248165967670414 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.30999999999999994 y[1] (analytic) 0.7085503006915412 y[1] (numeric) 0.7085503006915409 absolute error 3.3306690738754696e-16 relative error 4.7006811945810405e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.2031707286848104 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.29999999999999993 y[1] (analytic) 0.7328823955249676 y[1] (numeric) 0.7328823955249673 absolute error 3.3306690738754696e-16 relative error 4.5446160178123715e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.21385935275271278 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.2899999999999999 y[1] (analytic) 0.7571698923444602 y[1] (numeric) 0.7571698923444597 absolute error 4.440892098500626e-16 relative error 5.865119761629833e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.2245475338394347 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.2799999999999999 y[1] (analytic) 0.7814464258335736 y[1] (numeric) 0.7814464258335735 absolute error 1.1102230246251565e-16 relative error 1.4207282648210656e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.23523527388815796 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.2699999999999999 y[1] (analytic) 0.8057430393427546 y[1] (numeric) 0.8057430393427544 absolute error 2.220446049250313e-16 relative error 2.7557744104888988e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.2459225748260599 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.2599999999999999 y[1] (analytic) 0.8300886502211359 y[1] (numeric) 0.8300886502211355 absolute error 3.3306690738754696e-16 relative error 4.012425748729583e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.2566094385634067 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.2499999999999999 y[1] (analytic) 0.8545104320096022 y[1] (numeric) 0.8545104320096018 absolute error 4.440892098500626e-16 relative error 5.1970016188763436e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.267295866990511 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.23999999999999988 y[1] (analytic) 0.8790341320534293 y[1] (numeric) 0.879034132053429 absolute error 3.3306690738754696e-16 relative error 3.789009951291659e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.2779818619686784 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.22999999999999987 y[1] (analytic) 0.9036843384925536 y[1] (numeric) 0.9036843384925534 absolute error 2.220446049250313e-16 relative error 2.457103608716142e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.28866742530471245 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.21999999999999986 y[1] (analytic) 0.9284847072624044 y[1] (numeric) 0.9284847072624042 absolute error 2.220446049250313e-16 relative error 2.3914729363687625e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.2993525586814859 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.20999999999999985 y[1] (analytic) 0.9534581573030413 y[1] (numeric) 0.9534581573030411 absolute error 2.220446049250313e-16 relative error 2.328834288366763e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.3100372634737038 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.19999999999999984 y[1] (analytic) 0.9786270403695344 y[1] (numeric) 0.9786270403695341 absolute error 3.3306690738754696e-16 relative error 3.403410018813493e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.3207215402696635 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.18999999999999984 y[1] (analytic) 1.0040132904844299 y[1] (numeric) 1.0040132904844297 absolute error 2.220446049250313e-16 relative error 2.2115703749090437e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.33140538765398647 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.17999999999999983 y[1] (analytic) 1.0296385570503646 y[1] (numeric) 1.0296385570503641 absolute error 4.440892098500626e-16 relative error 4.3130592459771305e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.3420887991640516 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.16999999999999982 y[1] (analytic) 1.0555243248605362 y[1] (numeric) 1.0555243248605357 absolute error 4.440892098500626e-16 relative error 4.207285416266831e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.35277175580327963 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.1599999999999998 y[1] (analytic) 1.081692023644923 y[1] (numeric) 1.0816920236449228 absolute error 2.220446049250313e-16 relative error 2.0527525401991854e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.36345420789885724 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.1499999999999998 y[1] (analytic) 1.1081631293262126 y[1] (numeric) 1.1081631293262126 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.3741360317399458 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.1399999999999998 y[1] (analytic) 1.134959258798895 y[1] (numeric) 1.1349592587988953 absolute error 2.220446049250313e-16 relative error 1.9564103574961514e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.3848169272447977 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.12999999999999978 y[1] (analytic) 1.1621022597639503 y[1] (numeric) 1.1621022597639503 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.3954961792596828 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.11999999999999977 y[1] (analytic) 1.1896142969323518 y[1] (numeric) 1.1896142969323518 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.40617210671557114 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.10999999999999976 y[1] (analytic) 1.21751793573995 y[1] (numeric) 1.21751793573995 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.41684080397596995 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.09999999999999976 y[1] (analytic) 1.2458362245842622 y[1] (numeric) 1.245836224584262 absolute error 2.220446049250313e-16 relative error 1.7822936959400742e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.4274932910020661 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.08999999999999975 y[1] (analytic) 1.2745927764927867 y[1] (numeric) 1.2745927764927862 absolute error 4.440892098500626e-16 relative error 3.4841654373095834e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.43810911521126233 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.07999999999999974 y[1] (analytic) 1.3038118510569963 y[1] (numeric) 1.303811851056996 absolute error 2.220446049250313e-16 relative error 1.703041775122848e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.44864210152051387 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.06999999999999973 y[1] (analytic) 1.3335184374118536 y[1] (numeric) 1.3335184374118532 absolute error 4.440892098500626e-16 relative error 3.330206747736978e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.45898886359640156 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.05999999999999972 y[1] (analytic) 1.3637383390043267 y[1] (numeric) 1.363738339004327 absolute error 2.220446049250313e-16 relative error 1.628205342435026e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.4664200859265702 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.04999999999999971 y[1] (analytic) 1.394498260873555 y[1] (numeric) 1.3944982608735552 absolute error 2.220446049250313e-16 relative error 1.5922902964822343e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.46726383826510826 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.0399999999999997 y[1] (analytic) 1.425825900158274 y[1] (numeric) 1.425825900158274 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.4592447259895441 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.029999999999999694 y[1] (analytic) 1.4577500405526784 y[1] (numeric) 1.4577500405526782 absolute error 2.220446049250313e-16 relative error 1.523200814598141e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.43539186909182526 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.019999999999999685 y[1] (analytic) 1.490300651449258 y[1] (numeric) 1.4903006514492578 absolute error 2.220446049250313e-16 relative error 1.4899316101694096e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.3850072512656399 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.009999999999999676 y[1] (analytic) 1.5235089925359289 y[1] (numeric) 1.523508992535928 absolute error 8.881784197001252e-16 relative error 5.829820657781115e-14% Correct digits 16 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.2612801348363973e-16 y[1] (analytic) 1.5574077246549038 y[1] (numeric) 1.5574077246549027 absolute error 1.1102230246251565e-15 relative error 7.128660061520909e-14% Correct digits 16 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.010000000000000328 y[1] (analytic) 1.592031027782438 y[1] (numeric) 1.5920310277824374 absolute error 6.661338147750939e-16 relative error 4.1841760816870567e-14% Correct digits 16 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.020000000000000337 y[1] (analytic) 1.6274147270523647 y[1] (numeric) 1.627414727052364 absolute error 6.661338147750939e-16 relative error 4.0932025727800853e-14% Correct digits 16 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.030000000000000346 y[1] (analytic) 1.663596427822981 y[1] (numeric) 1.6635964278229796 absolute error 1.3322676295501878e-15 relative error 8.008358320975856e-14% Correct digits 16 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.040000000000000355 y[1] (analytic) 1.700615660877512 y[1] (numeric) 1.700615660877511 absolute error 1.1102230246251565e-15 relative error 6.528359406335733e-14% 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 0.005002456557985862 Order of pole (three term test) 0.16650594396451945 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.050000000000000364 y[1] (analytic) 1.7385140389543783 y[1] (numeric) 1.7385140389543776 absolute error 6.661338147750939e-16 relative error 3.831627469489618e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.49645642557672914 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.019292938657582828 Order of pole (three term test) 9.880832068556868 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.06000000000000037 y[1] (analytic) 1.7773354259266372 y[1] (numeric) 1.777335425926636 absolute error 1.1102230246251565e-15 relative error 6.246558800493875e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.5785865470282033 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.046982743810569196 Order of pole (three term test) 35.484122729301504 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.07000000000000038 y[1] (analytic) 1.8171261200923863 y[1] (numeric) 1.8171261200923845 absolute error 1.7763568394002505e-15 relative error 9.775638684396529e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.6172423971002053 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.10145473052586614 Order of pole (three term test) 89.68430258205633 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.08000000000000039 y[1] (analytic) 1.857935053202112 y[1] (numeric) 1.8579350532021106 absolute error 1.3322676295501878e-15 relative error 7.170689994001957e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.6314463457367527 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.19554509571479534 Order of pole (three term test) 186.24117280300027 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.0900000000000004 y[1] (analytic) 1.8998140070380727 y[1] (numeric) 1.8998140070380716 absolute error 1.1102230246251565e-15 relative error 5.843851137596689e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.6331378059326777 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.3224464232525748 Order of pole (three term test) 319.88519591395226 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; Iterations 500 Total Elapsed Time 5.0 Seconds Elapsed Time(since restart) 5.0 Seconds Time to Timeout 2 Minutes 55.0 Seconds Percent Done 100.20000000000009%