##############ECHO OF PROBLEM################# ##############R:Temp/mtest3postode.ode################# diff ( y2 , x , 1 ) = neg ( y1 ) + 1.0 ; diff ( y1 , x , 1 ) = y2 - 1.0 ; ! #BEGIN FIRST INPUT BLOCK # Digits:=16; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.1) x_end=c(0.5) $array_y1_init[0 + 1] = exact_soln_y1(x_start) $array_y2_init[0 + 1] = exact_soln_y2(x_start) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=3 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=12 $glob_max_minutes=(3.0) $glob_subiter_method=2 $glob_max_iter=1000000 $glob_upper_ratio_limit=c(1.000001) $glob_lower_ratio_limit=c(0.999999) $glob_look_poles=true $glob_h=c(0.001) $glob_display_interval=c(0.01) $glob_h_reason=1 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y1 (x) x = c(x) return(c(1.0) + cos(c(x))) end def exact_soln_y2 (x) x = c(x) return(c(1.0) - sin(c(x))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y2[1] (closed_form) 0.9001665833531718 y2[1] (numeric) 0.9001665833531718 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 y1[1] (closed_form) 1.9950041652780257 y1[1] (numeric) 1.9950041652780257 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09933466539753066 Order of pole (three term test) 32.990033288920614 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.09933466539753065 Order of pole (three term test) 32.00996671107938 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.11000000000000001 y2[1] (closed_form) 0.8902216991628251 y2[1] (numeric) 0.8902216991628249 absolute error 2.220446049250313e-16 relative error 2.494261880314136e-14% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 y1[1] (closed_form) 1.9939560979566968 y1[1] (numeric) 1.993956097956697 absolute error 2.220446049250313e-16 relative error 1.1135882337257634e-14% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10911481154043488 Order of pole (three term test) 32.9879487246653 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.1091148115404349 Order of pole (three term test) 32.0120512753347 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.12000000000000002 y2[1] (closed_form) 0.8802877927110806 y2[1] (numeric) 0.8802877927110802 absolute error 4.440892098500626e-16 relative error 5.044818450592978e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9928086358538661 y1[1] (numeric) 1.9928086358538664 absolute error 2.220446049250313e-16 relative error 1.1142294394458554e-14% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.11885131321356779 Order of pole (three term test) 32.98566898742602 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.1188513132135678 Order of pole (three term test) 32.01433101257399 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.13000000000000003 y2[1] (closed_form) 0.8703658573803051 y2[1] (numeric) 0.8703658573803046 absolute error 5.551115123125783e-16 relative error 6.37791002031486e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 h 0.001 y1[1] (closed_form) 1.991561893714788 y1[1] (numeric) 1.9915618937147883 absolute error 2.220446049250313e-16 relative error 1.1149269607225692e-14% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.12854027594607798 Order of pole (three term test) 32.983194989067265 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.12854027594607798 Order of pole (three term test) 32.01680501093275 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.14000000000000004 y2[1] (closed_form) 0.8604568853557635 y2[1] (numeric) 0.8604568853557629 absolute error 5.551115123125783e-16 relative error 6.451357665446103e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9902159962126371 y1[1] (numeric) 1.9902159962126371 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.13817782428205747 Order of pole (three term test) 32.980527719155376 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.13817782428205744 Order of pole (three term test) 32.01947228084462 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.15000000000000005 y2[1] (closed_form) 0.8505618675264007 y2[1] (numeric) 0.8505618675264002 absolute error 5.551115123125783e-16 relative error 6.526409582961325e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9887710779360424 y1[1] (numeric) 1.9887710779360424 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1477601033306704 Order of pole (three term test) 32.9776682445628 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.1477601033306704 Order of pole (three term test) 32.0223317554372 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.16000000000000006 y2[1] (closed_form) 0.840681793385754 y2[1] (numeric) 0.8406817933857534 absolute error 5.551115123125783e-16 relative error 6.603110911643839e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9872272833756268 y1[1] (numeric) 1.9872272833756266 absolute error 2.220446049250313e-16 relative error 1.1173588787884023e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1572832803080595 Order of pole (three term test) 32.97461770904122 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.15728328030805952 Order of pole (three term test) 32.02538229095879 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.17000000000000007 y2[1] (closed_form) 0.8308176509330039 y2[1] (numeric) 0.8308176509330035 absolute error 3.3306690738754696e-16 relative error 4.008905046895845e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9855847669095605 y1[1] (numeric) 1.9855847669095605 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1667435460704075 Order of pole (three term test) 32.97137733276417 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.16674354607040756 Order of pole (three term test) 32.02862266723583 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.18000000000000008 y2[1] (closed_form) 0.8209704265741757 y2[1] (numeric) 0.8209704265741753 absolute error 4.440892098500626e-16 relative error 5.409320427085306e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9838436927881213 y1[1] (numeric) 1.9838436927881213 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1761371166375453 Order of pole (three term test) 32.96794841183897 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.1761371166375453 Order of pole (three term test) 32.03205158816103 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.19000000000000009 y2[1] (closed_form) 0.8111411050234993 y2[1] (numeric) 0.811141105023499 absolute error 3.3306690738754696e-16 relative error 4.106152497078764e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9820042351172704 y1[1] (numeric) 1.98200423511727 absolute error 4.440892098500626e-16 relative error 2.2406067655238234e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.18546023470649176 Order of pole (three term test) 32.964332317788255 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.1854602347064918 Order of pole (three term test) 32.03566768221175 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2000000000000001 y2[1] (closed_form) 0.8013306692049387 y2[1] (numeric) 0.8013306692049383 absolute error 3.3306690738754696e-16 relative error 4.1564228125451386e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9800665778412416 y1[1] (numeric) 1.980066577841241 absolute error 6.661338147750939e-16 relative error 3.364199074060142e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1947091711543259 Order of pole (three term test) 32.96053049700144 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.19470917115432584 Order of pole (three term test) 32.03946950299856 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2100000000000001 y2[1] (closed_form) 0.7915401001539003 y2[1] (numeric) 0.7915401001539 absolute error 3.3306690738754696e-16 relative error 4.207833656472847e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9780309147241484 y1[1] (numeric) 1.9780309147241475 absolute error 8.881784197001252e-16 relative error 4.49021505725045e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2038802265297858 Order of pole (three term test) 32.956544470156146 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.20388022652978582 Order of pole (three term test) 32.04345552984385 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2200000000000001 y2[1] (closed_form) 0.7817703769191305 y2[1] (numeric) 0.7817703769191302 absolute error 3.3306690738754696e-16 relative error 4.2604186244575595e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9758974493306054 y1[1] (numeric) 1.9758974493306043 absolute error 1.1102230246251565e-15 relative error 5.6188291806403105e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.21296973253300047 Order of pole (three term test) 32.952375831609984 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.21296973253300044 Order of pole (three term test) 32.047624168390016 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.23000000000000012 y2[1] (closed_form) 0.7720224764648115 y2[1] (numeric) 0.7720224764648111 absolute error 3.3306690738754696e-16 relative error 4.314212572057519e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9736663950053748 y1[1] (numeric) 1.9736663950053734 absolute error 1.3322676295501878e-15 relative error 6.750216920760612e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2219740534827604 Order of pole (three term test) 32.948026248762766 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2219740534827604 Order of pole (three term test) 32.051973751237234 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.24000000000000013 y2[1] (closed_form) 0.7622973735728653 y2[1] (numeric) 0.7622973735728651 absolute error 2.220446049250313e-16 relative error 2.912834447852218e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.9713379748520294 y1[1] (numeric) 1.9713379748520279 absolute error 1.5543122344752192e-15 relative error 7.88455482673836e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2308895877707422 Order of pole (three term test) 32.94349746138964 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2308895877707422 Order of pole (three term test) 32.05650253861036 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2500000000000001 y2[1] (closed_form) 0.7525960407454769 y2[1] (numeric) 0.7525960407454767 absolute error 2.220446049250313e-16 relative error 2.950382315393091e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.9689124217106446 y1[1] (numeric) 1.9689124217106433 absolute error 1.3322676295501878e-15 relative error 6.766515436947051e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2397127693021019 Order of pole (three term test) 32.93879128094519 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.23971276930210186 Order of pole (three term test) 32.06120871905482 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2600000000000001 y2[1] (closed_form) 0.7429194481078447 y2[1] (numeric) 0.7429194481078446 absolute error 1.1102230246251565e-16 relative error 1.4944056552198278e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.9663899781345133 y1[1] (numeric) 1.9663899781345118 absolute error 1.5543122344752192e-15 relative error 7.904394610217519e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24844006892186885 Order of pole (three term test) 32.93390958983882 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.24844006892186887 Order of pole (three term test) 32.06609041016117 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y2[1] (closed_form) 0.7332685633111687 y2[1] (numeric) 0.7332685633111684 absolute error 3.3306690738754696e-16 relative error 4.5422226460049014e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9637708963658906 y1[1] (numeric) 1.9637708963658893 absolute error 1.3322676295501878e-15 relative error 6.78423146007333e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2570679958265572 Order of pole (three term test) 32.928854340681916 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.25706799582655726 Order of pole (three term test) 32.071145659318084 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y2[1] (closed_form) 0.7236443514358861 y2[1] (numeric) 0.7236443514358858 absolute error 3.3306690738754696e-16 relative error 4.602632587771346e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9610554383107708 y1[1] (numeric) 1.9610554383107694 absolute error 1.3322676295501878e-15 relative error 6.793625532064443e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.26559309896044236 Order of pole (three term test) 32.923627555506705 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2655930989604425 Order of pole (three term test) 32.076372444493295 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.29000000000000015 y2[1] (closed_form) 0.7140477748951644 y2[1] (numeric) 0.7140477748951638 absolute error 5.551115123125783e-16 relative error 7.774150859780763e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.958243875512697 y1[1] (numeric) 1.9582438755126954 absolute error 1.5543122344752192e-15 relative error 7.937276117195962e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2740119683959379 Order of pole (three term test) 32.918231324957596 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.27401196839593783 Order of pole (three term test) 32.081768675042404 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.30000000000000016 y2[1] (closed_form) 0.7044797933386603 y2[1] (numeric) 0.7044797933386596 absolute error 6.661338147750939e-16 relative error 9.455683769411786e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.955336489125606 y1[1] (numeric) 1.9553364891256042 absolute error 1.7763568394002505e-15 relative error 9.08466061611016e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.28232123669751874 Order of pole (three term test) 32.91266780745484 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2823212366975188 Order of pole (three term test) 32.08733219254516 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.31000000000000016 y2[1] (closed_form) 0.6949413635565563 y2[1] (numeric) 0.6949413635565559 absolute error 4.440892098500626e-16 relative error 6.390311947720483e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9523335698857134 y1[1] (numeric) 1.9523335698857118 absolute error 1.5543122344752192e-15 relative error 7.961304658436039e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2905175802686533 Order of pole (three term test) 32.90693922833126 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2905175802686533 Order of pole (three term test) 32.09306077166873 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3200000000000002 y2[1] (closed_form) 0.6854334393838821 y2[1] (numeric) 0.6854334393838818 absolute error 3.3306690738754696e-16 relative error 4.859215909963949e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.949235418082441 y1[1] (numeric) 1.9492354180824396 absolute error 1.3322676295501878e-15 relative error 6.834821577687139e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.29859772068119655 Order of pole (three term test) 32.901047878942144 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2985977206811965 Order of pole (three term test) 32.098952121057856 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3300000000000002 y2[1] (closed_form) 0.6759569716051315 y2[1] (numeric) 0.6759569716051311 absolute error 3.3306690738754696e-16 relative error 4.9273388895841157e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.946042343528387 y1[1] (numeric) 1.9460423435283858 absolute error 1.1102230246251565e-15 relative error 5.705030151667723e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.30655842598671756 Order of pole (three term test) 32.89499611574868 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.30655842598671756 Order of pole (three term test) 32.105003884251325 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3400000000000002 y2[1] (closed_form) 0.6665129078591854 y2[1] (numeric) 0.666512907859185 absolute error 3.3306690738754696e-16 relative error 4.9971561459679066e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.942754665528346 y1[1] (numeric) 1.9427546655283447 absolute error 1.3322676295501878e-15 relative error 6.857621567918707e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.31439651200923496 Order of pole (three term test) 32.888786359375466 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.31439651200923496 Order of pole (three term test) 32.11121364062454 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3500000000000002 y2[1] (closed_form) 0.6571021925445484 y2[1] (numeric) 0.657102192544548 absolute error 3.3306690738754696e-16 relative error 5.068723117446707e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.939372712847379 y1[1] (numeric) 1.9393727128473777 absolute error 1.3322676295501878e-15 relative error 6.869580151997488e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3221088436188462 Order of pole (three term test) 32.88242109364224 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3221088436188462 Order of pole (three term test) 32.11757890635776 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3600000000000002 y2[1] (closed_form) 0.6477257667249099 y2[1] (numeric) 0.6477257667249096 absolute error 3.3306690738754696e-16 relative error 5.14209754340375e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9358968236779348 y1[1] (numeric) 1.9358968236779337 absolute error 1.1102230246251565e-15 relative error 5.734928695816996e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3296923359857372 Order of pole (three term test) 32.87590286457045 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3296923359857372 Order of pole (three term test) 32.12409713542955 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3700000000000002 y2[1] (closed_form) 0.6383845680350377 y2[1] (numeric) 0.6383845680350375 absolute error 2.220446049250313e-16 relative error 3.4782263864630945e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9323273456060344 y1[1] (numeric) 1.9323273456060337 absolute error 6.661338147750939e-16 relative error 3.4473135014614974e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.337143955814073 Order of pole (three term test) 32.8692342793648 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.337143955814073 Order of pole (three term test) 32.13076572063521 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3800000000000002 y2[1] (closed_form) 0.6290795305870172 y2[1] (numeric) 0.6290795305870168 absolute error 3.3306690738754696e-16 relative error 5.294511920881451e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.92866463557651 y1[1] (numeric) 1.9286646355765094 absolute error 6.661338147750939e-16 relative error 3.45386026418209e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.34446072255527616 Order of pole (three term test) 32.86241800537046 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.34446072255527616 Order of pole (three term test) 32.13758199462955 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.39000000000000024 y2[1] (closed_form) 0.6198115848768384 y2[1] (numeric) 0.619811584876838 absolute error 4.440892098500626e-16 relative error 7.164906572991964e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9249090598573129 y1[1] (numeric) 1.924909059857312 absolute error 8.881784197001252e-16 relative error 4.614131847693433e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3516397096002056 Order of pole (three term test) 32.85545676900613 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3516397096002056 Order of pole (three term test) 32.14454323099386 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.40000000000000024 y2[1] (closed_form) 0.6105816576913493 y2[1] (numeric) 0.6105816576913489 absolute error 4.440892098500626e-16 relative error 7.273215699423302e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.921060994002885 y1[1] (numeric) 1.9210609940028844 absolute error 6.661338147750939e-16 relative error 3.4675307908213846e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.35867804544976173 Order of pole (three term test) 32.84835335467358 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.35867804544976184 Order of pole (three term test) 32.151646645326416 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.41000000000000025 y2[1] (closed_form) 0.6013906720155768 y2[1] (numeric) 0.6013906720155764 absolute error 4.440892098500626e-16 relative error 7.384371432993561e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.917120822816605 y1[1] (numeric) 1.9171208228166046 absolute error 4.440892098500626e-16 relative error 2.316438299374441e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.36557291486344834 Order of pole (three term test) 32.841110603643806 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.36557291486344834 Order of pole (three term test) 32.158889396356194 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.42000000000000026 y2[1] (closed_form) 0.5922395469404296 y2[1] (numeric) 0.5922395469404291 absolute error 4.440892098500626e-16 relative error 7.498472740367865e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9130889403123081 y1[1] (numeric) 1.9130889403123077 absolute error 4.440892098500626e-16 relative error 2.321320250680901e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3723215599854303 Order of pole (three term test) 32.833731412920656 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3723215599854303 Order of pole (three term test) 32.16626858707935 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.43000000000000027 y2[1] (closed_form) 0.5831291975707891 y2[1] (numeric) 0.5831291975707886 absolute error 4.440892098500626e-16 relative error 7.615622947711383e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.908965749674885 y1[1] (numeric) 1.9089657496748846 absolute error 4.440892098500626e-16 relative error 2.3263340891563677e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3789212814476389 Order of pole (three term test) 32.82621873408202 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.378921281447639 Order of pole (three term test) 32.173781265917974 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4400000000000003 y2[1] (closed_form) 0.5740605349340002 y2[1] (numeric) 0.5740605349339998 absolute error 4.440892098500626e-16 relative error 7.735929972979585e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9047516632199633 y1[1] (numeric) 1.9047516632199628 absolute error 4.440892098500626e-16 relative error 2.3314808876414595e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3853694394494854 Order of pole (three term test) 32.81857557209929 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.38536943944948526 Order of pole (three term test) 32.18142442790071 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4500000000000003 y2[1] (closed_form) 0.5650344658887696 y2[1] (numeric) 0.5650344658887692 absolute error 4.440892098500626e-16 relative error 7.85950657278107e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9004471023526768 y1[1] (numeric) 1.9004471023526763 absolute error 4.440892098500626e-16 relative error 2.3367617509600666e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.39166345481374204 Order of pole (three term test) 32.81080498413533 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3916634548137421 Order of pole (three term test) 32.18919501586467 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4600000000000003 y2[1] (closed_form) 0.55605189303448 y2[1] (numeric) 0.5560518930344795 absolute error 4.440892098500626e-16 relative error 7.986470604867185e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.896052497525525 y1[1] (numeric) 1.8960524975255242 absolute error 8.881784197001252e-16 relative error 4.6843556328701725e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3978008100181838 Order of pole (three term test) 32.80291007832174 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3978008100181838 Order of pole (three term test) 32.19708992167827 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4700000000000003 y2[1] (closed_form) 0.5471137146209315 y2[1] (numeric) 0.5471137146209312 absolute error 3.3306690738754696e-16 relative error 6.087708980541876e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.8915682881953289 y1[1] (numeric) 1.891568288195328 absolute error 8.881784197001252e-16 relative error 4.695460508843175e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.40377905020255755 Order of pole (three term test) 32.79489401251554 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4037790502025576 Order of pole (three term test) 32.20510598748445 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4800000000000003 y2[1] (closed_form) 0.5382208244585168 y2[1] (numeric) 0.5382208244585166 absolute error 2.220446049250313e-16 relative error 4.125529798079103e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.8869949227792842 y1[1] (numeric) 1.8869949227792833 absolute error 8.881784197001252e-16 relative error 4.7068405377157054e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4095957841504996 Order of pole (three term test) 32.78675999303623 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4095957841504995 Order of pole (three term test) 32.21324000696377 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4900000000000003 y2[1] (closed_form) 0.5293741118288418 y2[1] (numeric) 0.5293741118288415 absolute error 2.220446049250313e-16 relative error 4.194474190623496e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.8823328586101213 y1[1] (numeric) 1.8823328586101205 absolute error 8.881784197001252e-16 relative error 4.7184981956694906e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.41524868524598546 Order of pole (three term test) 32.77851127338311 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4152486852459855 Order of pole (three term test) 32.2214887266169 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y2 , x , 1 ) = neg ( y1 ) + 1.0 ; diff ( y1 , x , 1 ) = y2 - 1.0 ; Iterations 400 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.25000000000009%