##############ECHO OF PROBLEM################# ##############temp/lin_tanhpostode.ode################# diff ( y , x , 1 ) = tanh (3.0 * 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=1.1 x_end=2.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=10 #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(ln(cosh(3.0*x + 1.0))/3.0) 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 0.8999999999999999 estimated_steps 900000.0 step_error 1.1111111111111112e-16 est_needed_step_err 1.1111111111111112e-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 4.114948349378717e-163 estimated_step_error 4.114948349378717e-163 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 2.7614941745065305e-155 estimated_step_error 2.7614941745065305e-155 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 1.8532061392314484e-147 estimated_step_error 1.8532061392314484e-147 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 1.2436639357936756e-139 estimated_step_error 1.2436639357936756e-139 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 8.346065222575855e-132 estimated_step_error 8.346065222575855e-132 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 5.600919803289607e-124 estimated_step_error 5.600919803289607e-124 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 3.7586737158978683e-116 estimated_step_error 3.7586737158978683e-116 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 2.522349630320909e-108 estimated_step_error 2.522349630320909e-108 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 1.6926482438364402e-100 estimated_step_error 1.6926482438364402e-100 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 1.1358204636977879e-92 estimated_step_error 1.1358204636977879e-92 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 7.621066599549855e-85 estimated_step_error 7.621066599549855e-85 best_h 0.002048 opt_iter 12 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.112673208506e-77 estimated_step_error 5.112673208506e-77 best_h 0.004096 opt_iter 13 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.4287262949855774e-69 estimated_step_error 3.4287262949855774e-69 best_h 0.008192 opt_iter 14 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.2978568146631016e-61 estimated_step_error 2.2978568146631016e-61 best_h 0.016384 opt_iter 15 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.5378898804652407e-53 estimated_step_error 1.5378898804652407e-53 best_h 0.032768 opt_iter 16 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0264965592831055e-45 estimated_step_error 1.0264965592831055e-45 best_h 0.065536 opt_iter 17 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.815117159449936e-38 estimated_step_error 6.815117159449936e-38 best_h 0.131072 opt_iter 18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.477716319818289e-30 estimated_step_error 4.477716319818289e-30 best_h 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] 1.1 y[1] (analytic) 1.2023456360961104 y[1] (numeric) 1.2023456360961104 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5000248574835989 Order of pole (three term test) -249.52490811220153 Radius of convergence (six term test) for eq 1 1.5274316090026347 Order of pole (six term test) 0.03164330921283032 TOP MAIN SOLVE Loop x[1] 1.11 y[1] (analytic) 1.212342062905879 y[1] (numeric) 1.2123420629058792 absolute error 2.220446049250313e-16 relative error 1.831534281610337e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.7125026532634249 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.47034706228458867 Order of pole (three term test) -239.39570936394512 Radius of convergence (six term test) for eq 1 1.5381067232714345 Order of pole (six term test) 0.049236153403033 TOP MAIN SOLVE Loop x[1] 1.12 y[1] (analytic) 1.222338697767025 y[1] (numeric) 1.2223386977670252 absolute error 2.220446049250313e-16 relative error 1.8165554713326478e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.6977171587687254 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.43769944912950604 Order of pole (three term test) -227.54129880316663 Radius of convergence (six term test) for eq 1 1.549145406504964 Order of pole (six term test) 0.07192451068031858 TOP MAIN SOLVE Loop x[1] 1.1300000000000001 y[1] (analytic) 1.2323355285675388 y[1] (numeric) 1.232335528567539 absolute error 2.220446049250313e-16 relative error 1.8018193891004258e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.40291264879241767 Order of pole (three term test) -214.30990673904842 Radius of convergence (six term test) for eq 1 1.5605806858473537 Order of pole (six term test) 0.10020399590927376 TOP MAIN SOLVE Loop x[1] 1.1400000000000001 y[1] (analytic) 1.242332543900312 y[1] (numeric) 1.2423325439003123 absolute error 4.440892098500626e-16 relative error 3.574640397456235e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3667885705518177 Order of pole (three term test) -200.04909562054422 Radius of convergence (six term test) for eq 1 1.5724418838841507 Order of pole (six term test) 0.13452067441195759 TOP MAIN SOLVE Loop x[1] 1.1500000000000001 y[1] (analytic) 1.2523297330221377 y[1] (numeric) 1.252329733022138 absolute error 2.220446049250313e-16 relative error 1.7730522487012306e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.33007356865884685 Order of pole (three term test) -185.09196184369173 Radius of convergence (six term test) for eq 1 1.584753712330393 Order of pole (six term test) 0.17525881886630224 TOP MAIN SOLVE Loop x[1] 1.1600000000000001 y[1] (analytic) 1.262327085815092 y[1] (numeric) 1.2623270858150921 absolute error 2.220446049250313e-16 relative error 1.759010064983719e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.29344017670037137 Order of pole (three term test) -169.7469086876739 Radius of convergence (six term test) for eq 1 1.597535402734142 Order of pole (six term test) 0.22272900834025045 TOP MAIN SOLVE Loop x[1] 1.1700000000000002 y[1] (analytic) 1.2723245927501607 y[1] (numeric) 1.272324592750161 absolute error 2.220446049250313e-16 relative error 1.7451883441557665e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2574768714480165 Order of pole (three term test) -154.29096690432144 Radius of convergence (six term test) for eq 1 1.6107998882063894 Order of pole (six term test) 0.2771566630020885 TOP MAIN SOLVE Loop x[1] 1.1800000000000002 y[1] (analytic) 1.2823222448529796 y[1] (numeric) 1.2823222448529796 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.6247132709852057 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.22268467774666525 Order of pole (three term test) -138.9662957307884 Radius of convergence (six term test) for eq 1 1.624553049477552 Order of pole (six term test) 0.3386711053687801 TOP MAIN SOLVE Loop x[1] 1.1900000000000002 y[1] (analytic) 1.2923200336715641 y[1] (numeric) 1.2923200336715646 absolute error 4.440892098500626e-16 relative error 3.4363717831439683e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.6142590568242492 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.18947911351969504 Order of pole (three term test) -123.9793002132404 Radius of convergence (six term test) for eq 1 1.6387930377180906 Order of pole (six term test) 0.4072952422628209 TOP MAIN SOLVE Loop x[1] 1.2000000000000002 y[1] (analytic) 1.3023179512459186 y[1] (numeric) 1.3023179512459189 absolute error 2.220446049250313e-16 relative error 1.7049953485829076e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.6040891855164026 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.1581959322670865 Order of pole (three term test) -109.50173044202324 Radius of convergence (six term test) for eq 1 1.6535096865350392 Order of pole (six term test) 0.48293598415008 TOP MAIN SOLVE Loop x[1] 1.2100000000000002 y[1] (analytic) 1.3123159900794066 y[1] (numeric) 1.3123159900794066 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.594140083567774 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.12909926157146642 Order of pole (three term test) -95.67315046873061 Radius of convergence (six term test) for eq 1 1.6686840260057099 Order of pole (six term test) 0.5653755551956827 TOP MAIN SOLVE Loop x[1] 1.2200000000000002 y[1] (analytic) 1.3223141431117904 y[1] (numeric) 1.3223141431117906 absolute error 2.220446049250313e-16 relative error 1.679212205977739e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.5843519439749882 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.10239097629630374 Order of pole (three term test) -82.60424333869841 Radius of convergence (six term test) for eq 1 1.6842879124677217 Order of pole (six term test) 0.6542638953682438 TOP MAIN SOLVE Loop x[1] 1.2300000000000002 y[1] (analytic) 1.3323124036938379 y[1] (numeric) 1.332312403693838 absolute error 2.220446049250313e-16 relative error 1.6666106560999683e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.5746679102038776 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.07822041799805561 Order of pole (three term test) -70.38052323101651 Radius of convergence (six term test) for eq 1 1.700283789260983 Order of pole (six term test) 0.7491124178119133 TOP MAIN SOLVE Loop x[1] 1.2400000000000002 y[1] (analytic) 1.3423107655634017 y[1] (numeric) 1.342310765563402 absolute error 2.220446049250313e-16 relative error 1.654196707808073e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.5650333526989735 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.05669383324899136 Order of pole (three term test) -59.06613414318079 Radius of convergence (six term test) for eq 1 1.716624595140745 Order of pole (six term test) 0.8492894501408106 TOP MAIN SOLVE Loop x[1] 1.2500000000000002 y[1] (analytic) 1.352309222822895 y[1] (numeric) 1.352309222822895 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.5553952164419549 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.03788312813022745 Order of pole (three term test) -48.707513191657945 Radius of convergence (six term test) for eq 1 1.7332538386712588 Order of pole (six term test) 0.9540177556133038 TOP MAIN SOLVE Loop x[1] 1.2600000000000002 y[1] (analytic) 1.3623077699180726 y[1] (numeric) 1.3623077699180723 absolute error 2.220446049250313e-16 relative error 1.6299151324548694e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.545701421580231 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.021833714373320906 Order of pole (three term test) -39.336778721957835 Radius of convergence (six term test) for eq 1 1.7501058583450633 Order of pole (six term test) 1.0623745935048543 TOP MAIN SOLVE Loop x[1] 1.2700000000000002 y[1] (analytic) 1.3723064016180493 y[1] (numeric) 1.3723064016180495 absolute error 2.220446049250313e-16 relative error 1.6180395621795872e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.5359003017544364 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.008571354547760889 Order of pole (three term test) -30.974767167003943 Radius of convergence (six term test) for eq 1 1.767106288331148 Order of pole (six term test) 1.1732948181292944 TOP MAIN SOLVE Loop x[1] 1.2800000000000002 y[1] (analytic) 1.382305112996481 y[1] (numeric) 1.382305112996481 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.525940066611349 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.7841727494689923 Order of pole (six term test) 1.2855775406024357 TOP MAIN SOLVE Loop x[1] 1.2900000000000003 y[1] (analytic) 1.3923038994138357 y[1] (numeric) 1.3923038994138355 absolute error 2.220446049250313e-16 relative error 1.5947998495049306e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.5157682762701334 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8012157825784854 Order of pole (six term test) 1.3978968571288366 TOP MAIN SOLVE Loop x[1] 1.3000000000000003 y[1] (analytic) 1.4023027565007016 y[1] (numeric) 1.4023027565007016 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.5053313162779927 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8181400366056506 Order of pole (six term test) 1.5088170800475549 TOP MAIN SOLVE Loop x[1] 1.3100000000000003 y[1] (analytic) 1.4123016801420638 y[1] (numeric) 1.412301680142064 absolute error 2.220446049250313e-16 relative error 1.5722179478161904e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.4945738618743993 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8348457182350162 Order of pole (six term test) 1.6168128011166996 TOP MAIN SOLVE Loop x[1] 1.3200000000000003 y[1] (analytic) 1.4223006664624958 y[1] (numeric) 1.4223006664624958 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.4834383203344697 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8512302989285025 Order of pole (six term test) 1.7202939149313412 TOP MAIN SOLVE Loop x[1] 1.3300000000000003 y[1] (analytic) 1.4322997118122114 y[1] (numeric) 1.4322997118122114 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.4718642396091064 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8671904650649895 Order of pole (six term test) 1.8176355102439494 TOP MAIN SOLVE Loop x[1] 1.3400000000000003 y[1] (analytic) 1.4422988127539318 y[1] (numeric) 1.4422988127539318 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.4597876705335115 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8826242822175943 Order of pole (six term test) 1.907212230483287 TOP MAIN SOLVE Loop x[1] 1.3500000000000003 y[1] (analytic) 1.4522979660505129 y[1] (numeric) 1.452297966050513 absolute error 2.220446049250313e-16 relative error 1.528919065616238e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.4471404684575724 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.003242357261843214 Order of pole (three term test) -0.9451996246727387 Radius of convergence (six term test) for eq 1 1.8974335293787297 Order of pole (six term test) 1.9874363700493038 TOP MAIN SOLVE Loop x[1] 1.3600000000000003 y[1] (analytic) 1.4622971686532964 y[1] (numeric) 1.4622971686532964 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.4338495181975142 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.015212429996953082 Order of pole (three term test) -1.7789836084203219 Radius of convergence (six term test) for eq 1 1.91152614386179 Order of pole (six term test) 2.056798633093898 TOP MAIN SOLVE Loop x[1] 1.3700000000000003 y[1] (analytic) 1.4722964176911344 y[1] (numeric) 1.4722964176911344 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.4198358635434147 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.030040156234529065 Order of pole (three term test) -3.6298761135251856 Radius of convergence (six term test) for eq 1 1.9248187023464305 Order of pole (six term test) 2.1139101391448527 TOP MAIN SOLVE Loop x[1] 1.3800000000000003 y[1] (analytic) 1.4822957104600574 y[1] (numeric) 1.4822957104600574 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.4050137192101033 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.04776026999003232 Order of pole (three term test) -6.501964507854032 Radius of convergence (six term test) for eq 1 1.937238851849566 Order of pole (six term test) 2.15754398862569 TOP MAIN SOLVE Loop x[1] 1.3900000000000003 y[1] (analytic) 1.4922950444135399 y[1] (numeric) 1.4922950444135399 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.3892893386612915 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.06841615461551605 Order of pole (three term test) -10.401917824330754 Radius of convergence (six term test) for eq 1 1.9487275956316508 Order of pole (six term test) 2.1866745031760466 TOP MAIN SOLVE Loop x[1] 1.4000000000000004 y[1] (analytic) 1.5022944171533352 y[1] (numeric) 1.5022944171533352 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.3725597056436 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.09206007335325911 Order of pole (three term test) -15.33915673402608 Radius of convergence (six term test) for eq 1 1.9592413368577113 Order of pole (six term test) 2.200512199891403 TOP MAIN SOLVE Loop x[1] 1.4100000000000004 y[1] (analytic) 1.5122938264208419 y[1] (numeric) 1.5122938264208419 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.354711009967632 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.11875328599355059 Order of pole (three term test) -21.325968021924975 Radius of convergence (six term test) for eq 1 1.9687535855283331 Order of pole (six term test) 2.198532627676922 TOP MAIN SOLVE Loop x[1] 1.4200000000000004 y[1] (analytic) 1.5222932700889737 y[1] (numeric) 1.5222932700889735 absolute error 2.220446049250313e-16 relative error 1.4586191063700454e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.3356168588205395 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.1485660646516931 Order of pole (three term test) -28.377571623845455 Radius of convergence (six term test) for eq 1 1.977256244994601 Order of pole (six term test) 2.18049743894991 TOP MAIN SOLVE Loop x[1] 1.4300000000000004 y[1] (analytic) 1.532292746154502 y[1] (numeric) 1.532292746154502 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.3151361627865479 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.18157761545499135 Order of pole (three term test) -36.512145744797316 Radius of convergence (six term test) for eq 1 1.9847604107423271 Order of pole (six term test) 2.14646644886216 TOP MAIN SOLVE Loop x[1] 1.4400000000000004 y[1] (analytic) 1.5422922527308458 y[1] (numeric) 1.5422922527308458 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.2931106200940587 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.2178759072969056 Order of pole (three term test) -45.7508133066065 Radius of convergence (six term test) for eq 1 1.9912966359326905 Order of pole (six term test) 2.0967999306130096 TOP MAIN SOLVE Loop x[1] 1.4500000000000004 y[1] (analytic) 1.5522917880412788 y[1] (numeric) 1.5522917880412785 absolute error 2.220446049250313e-16 relative error 1.4304308419051344e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.2693617021917776 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.25755740349986583 Order of pole (three term test) -56.11759088064873 Radius of convergence (six term test) for eq 1 1.9969146446574184 Order of pole (six term test) 2.0321509800480264 TOP MAIN SOLVE Loop x[1] 1.4600000000000004 y[1] (analytic) 1.5622913504125326 y[1] (numeric) 1.5622913504125326 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.2436870167355814 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.30072668718928236 Order of pole (three term test) -67.63929932486569 Radius of convergence (six term test) for eq 1 2.0016825003020746 Order of pole (six term test) 1.9534483639800566 TOP MAIN SOLVE Loop x[1] 1.4700000000000004 y[1] (analytic) 1.5722909382687755 y[1] (numeric) 1.5722909382687755 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.2158558882282258 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.3474959663724167 Order of pole (three term test) -80.345433535732 Radius of convergence (six term test) for eq 1 2.0056852636114963 Order of pole (six term test) 1.8618708309394076 TOP MAIN SOLVE Loop x[1] 1.4800000000000004 y[1] (analytic) 1.5822905501259366 y[1] (numeric) 1.5822905501259363 absolute error 2.220446049250313e-16 relative error 1.4033111991180033e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.1856039485916212 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.3979844396752518 Order of pole (three term test) -94.26798691011373 Radius of convergence (six term test) for eq 1 2.0090231986455267 Order of pole (six term test) 1.758814328264057 TOP MAIN SOLVE Loop x[1] 1.4900000000000004 y[1] (analytic) 1.5922901845863635 y[1] (numeric) 1.5922901845863633 absolute error 2.220446049250313e-16 relative error 1.3944983588698868e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.152626464843485 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.4523174989391685 Order of pole (three term test) -109.4412244199155 Radius of convergence (six term test) for eq 1 2.011809602791651 Order of pole (six term test) 1.645853891731056 TOP MAIN SOLVE Loop x[1] 1.5000000000000004 y[1] (analytic) 1.6022898403337917 y[1] (numeric) 1.6022898403337913 absolute error 4.440892098500626e-16 relative error 2.7715909985271404e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.1165700423852503 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.5106257394285115 Order of pole (three term test) -125.9013963428492 Radius of convergence (six term test) for eq 1 2.014168350622271 Order of pole (six term test) 1.5247021676225465 TOP MAIN SOLVE Loop x[1] 1.5100000000000005 y[1] (analytic) 1.6122895161286035 y[1] (numeric) 1.6122895161286033 absolute error 2.220446049250313e-16 relative error 1.3772005753544826e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.0770222192491719 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.5730437435610489 Order of pole (three term test) -143.68638303390836 Radius of convergence (six term test) for eq 1 2.016231246416238 Order of pole (six term test) 1.3971665320307274 TOP MAIN SOLVE Loop x[1] 1.5200000000000005 y[1] (analytic) 1.6222892108033673 y[1] (numeric) 1.6222892108033673 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.033498294883043 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.6397085981663044 Order of pole (three term test) -162.83525917749577 Radius of convergence (six term test) for eq 1 2.01813527992319 Order of pole (six term test) 1.2651066517446363 TOP MAIN SOLVE Loop x[1] 1.5300000000000005 y[1] (analytic) 1.6322889232586333 y[1] (numeric) 1.632288923258633 absolute error 2.220446049250313e-16 relative error 1.360326604935545e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.9854244927702269 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.7107581002038719 Order of pole (three term test) -183.3877642576731 Radius of convergence (six term test) for eq 1 2.020019873750203 Order of pole (six term test) 1.1303940858901615 TOP MAIN SOLVE Loop x[1] 1.5400000000000005 y[1] (analytic) 1.6422886524589737 y[1] (numeric) 1.6422886524589737 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.9321162054233495 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.7863286000426646 Order of pole (three term test) -205.38366407359 Radius of convergence (six term test) for eq 1 2.022024199933317 Order of pole (six term test) 0.994875202097182 TOP MAIN SOLVE Loop x[1] 1.5500000000000005 y[1] (analytic) 1.652288397429258 y[1] (numeric) 1.6522883974292577 absolute error 2.220446049250313e-16 relative error 1.343861067296141e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.8727495569370234 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.8665524265618815 Order of pole (three term test) -228.86198651446668 Radius of convergence (six term test) for eq 1 2.0242846287862517 Order of pole (six term test) 0.8603383018019475 TOP MAIN SOLVE Loop x[1] 1.5600000000000005 y[1] (analytic) 1.6622881572511379 y[1] (numeric) 1.6622881572511379 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.8063237562478213 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.9515548337382796 Order of pole (three term test) -253.86011323485363 Radius of convergence (six term test) for eq 1 2.026932358836117 Order of pole (six term test) 0.7284854914868522 TOP MAIN SOLVE Loop x[1] 1.5700000000000005 y[1] (analytic) 1.6722879310597447 y[1] (numeric) 1.6722879310597445 absolute error 2.220446049250313e-16 relative error 1.327789316665818e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.7316105599343721 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.0414504050139088 Order of pole (three term test) -280.4127076987674 Radius of convergence (six term test) for eq 1 2.030091260096267 Order of pole (six term test) 0.6009094742651531 TOP MAIN SOLVE Loop x[1] 1.5800000000000005 y[1] (analytic) 1.6822877180405724 y[1] (numeric) 1.6822877180405722 absolute error 2.220446049250313e-16 relative error 1.3198967248221696e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.1363388496606046 Order of pole (three term test) -308.55045920397447 Radius of convergence (six term test) for eq 1 2.0338759479703192 Order of pole (six term test) 0.47907513096514975 TOP MAIN SOLVE Loop x[1] 1.5900000000000005 y[1] (analytic) 1.6922875174265464 y[1] (numeric) 1.6922875174265462 absolute error 2.220446049250313e-16 relative error 1.3120973985714526e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2363001283142834 Order of pole (three term test) -338.29862318388024 Radius of convergence (six term test) for eq 1 2.0383900933178136 Order of pole (six term test) 0.364305537845782 TOP MAIN SOLVE Loop x[1] 1.6000000000000005 y[1] (analytic) 1.7022873284952613 y[1] (numeric) 1.702287328495261 absolute error 2.220446049250313e-16 relative error 1.3043896950188067e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.3413888463851393 Order of pole (three term test) -369.67533827661896 Radius of convergence (six term test) for eq 1 2.043724961480496 Order of pole (six term test) 0.25777186794053364 TOP MAIN SOLVE Loop x[1] 1.6100000000000005 y[1] (analytic) 1.71228715056638 y[1] (numeric) 1.7122871505663797 absolute error 2.220446049250313e-16 relative error 1.296772009598885e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.4516278679778072 Order of pole (three term test) -402.689704572516 Radius of convergence (six term test) for eq 1 2.04995816581666 Order of pole (six term test) 0.16048652816937725 TOP MAIN SOLVE Loop x[1] 1.6200000000000006 y[1] (analytic) 1.722286982999183 y[1] (numeric) 1.722286982999183 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5670011160141366 Order of pole (three term test) -437.3396110739548 Radius of convergence (six term test) for eq 1 2.0571526147566495 Order of pole (six term test) 0.0732988284520868 TOP MAIN SOLVE Loop x[1] 1.6300000000000006 y[1] (analytic) 1.732286825190263 y[1] (numeric) 1.732286825190263 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6874455520641192 Order of pole (three term test) -473.6093084668689 Radius of convergence (six term test) for eq 1 2.0653556276573335 Order of pole (six term test) -0.0031075248287777413 TOP MAIN SOLVE Loop x[1] 1.6400000000000006 y[1] (analytic) 1.742286676571351 y[1] (numeric) 1.7422866765713507 absolute error 2.220446049250313e-16 relative error 1.2744435683913584e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8128423632843316 Order of pole (three term test) -511.4667331639989 Radius of convergence (six term test) for eq 1 2.074598192918053 Order of pole (six term test) -0.06821578356531433 TOP MAIN SOLVE Loop x[1] 1.6500000000000006 y[1] (analytic) 1.7522865366072697 y[1] (numeric) 1.7522865366072695 absolute error 2.220446049250313e-16 relative error 1.2671706383988325e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.943007433233896 Order of pole (three term test) -550.8606031629498 Radius of convergence (six term test) for eq 1 2.084894342506459 Order of pole (six term test) -0.12167695861989358 TOP MAIN SOLVE Loop x[1] 1.6600000000000006 y[1] (analytic) 1.7622864047940086 y[1] (numeric) 1.762286404794008 absolute error 4.440892098500626e-16 relative error 2.5199604822575458e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.8009304316467546 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 2.077681235325503 Order of pole (three term test) -591.7173246837099 Radius of convergence (six term test) for eq 1 2.0962406180254156 Order of pole (six term test) -0.16331058622011163 TOP MAIN SOLVE Loop x[1] 1.6700000000000006 y[1] (analytic) 1.772286280656906 y[1] (numeric) 1.7722862806569057 absolute error 2.220446049250313e-16 relative error 1.2528709799792022e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.8898609674855058 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 2.2165183641974195 Order of pole (three term test) -633.9377713551362 Radius of convergence (six term test) for eq 1 2.108615608072728 Order of pole (six term test) -0.19310585960036342 TOP MAIN SOLVE Loop x[1] 1.6800000000000006 y[1] (analytic) 1.7822861637489436 y[1] (numeric) 1.7822861637489433 absolute error 2.220446049250313e-16 relative error 1.2458414896627619e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3590770173276248 Order of pole (three term test) -677.3940270466006 Radius of convergence (six term test) for eq 1 2.1219795402522807 Order of pole (six term test) -0.21122341902219333 TOP MAIN SOLVE Loop x[1] 1.6900000000000006 y[1] (analytic) 1.7922860536491336 y[1] (numeric) 1.7922860536491332 absolute error 4.440892098500626e-16 relative error 2.477780870670099e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.504808841816222 Order of pole (three term test) -721.9262143879837 Radius of convergence (six term test) for eq 1 2.1362739176507346 Order of pole (six term test) -0.21799796139217165 TOP MAIN SOLVE Loop x[1] 1.7000000000000006 y[1] (analytic) 1.8022859499610036 y[1] (numeric) 1.8022859499610036 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.6530496846328124 Order of pole (three term test) -767.3395687633168 Radius of convergence (six term test) for eq 1 2.1514211969759605 Order of pole (six term test) -0.21394169458729806 TOP MAIN SOLVE Loop x[1] 1.7100000000000006 y[1] (analytic) 1.8122858523111711 y[1] (numeric) 1.812285852311171 absolute error 2.220446049250313e-16 relative error 1.2252184424541104e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.8030119036095402 Order of pole (three term test) -813.401954128385 Radius of convergence (six term test) for eq 1 2.1673245126103557 Order of pole (six term test) -0.19974853071888354 TOP MAIN SOLVE Loop x[1] 1.7200000000000006 y[1] (analytic) 1.8222857603479958 y[1] (numeric) 1.8222857603479956 absolute error 2.220446049250313e-16 relative error 1.2184949789797413e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.9537790115447606 Order of pole (three term test) -859.8420529802997 Radius of convergence (six term test) for eq 1 2.1838674616700646 Order of pole (six term test) -0.17629874255566236 TOP MAIN SOLVE Loop x[1] 1.7300000000000006 y[1] (analytic) 1.832285673740316 y[1] (numeric) 1.8322856737403157 absolute error 2.220446049250313e-16 relative error 1.2118449001009926e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.104303522145209 Order of pole (three term test) -906.3484935213187 Radius of convergence (six term test) for eq 1 2.200913973125009 Order of pole (six term test) -0.14466367226003207 TOP MAIN SOLVE Loop x[1] 1.7400000000000007 y[1] (analytic) 1.8422855921762542 y[1] (numeric) 1.8422855921762538 absolute error 4.440892098500626e-16 relative error 2.4105340221733437e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.2534089199161405 Order of pole (three term test) -952.5701953799164 Radius of convergence (six term test) for eq 1 2.2183082957595115 Order of pole (six term test) -0.10610991393393654 TOP MAIN SOLVE Loop x[1] 1.7500000000000007 y[1] (analytic) 1.8522855153620947 y[1] (numeric) 1.8522855153620947 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.39979667062764 Order of pole (three term test) -998.1182162848232 Radius of convergence (six term test) for eq 1 2.2358751493271476 Order of pole (six term test) -0.06210222239116803 TOP MAIN SOLVE Loop x[1] 1.7600000000000007 y[1] (analytic) 1.8622854430212283 y[1] (numeric) 1.862285443021228 absolute error 4.440892098500626e-16 relative error 2.3846463038963916e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.5420590990769742 Order of pole (three term test) -1042.5693578051719 Radius of convergence (six term test) for eq 1 2.253420093149993 Order of pole (six term test) -0.014304264207799733 TOP MAIN SOLVE Loop x[1] 1.7700000000000007 y[1] (analytic) 1.8722853748931512 y[1] (numeric) 1.872285374893151 absolute error 2.220446049250313e-16 relative error 1.185954918532134e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.6786987724777447 Order of pole (three term test) -1085.4717349895298 Radius of convergence (six term test) for eq 1 2.270730175542347 Order of pole (six term test) 0.03542383060784893 TOP MAIN SOLVE Loop x[1] 1.7800000000000007 y[1] (analytic) 1.8822853107325317 y[1] (numeric) 1.8822853107325315 absolute error 2.220446049250313e-16 relative error 1.1796543470799222e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.808154717349001 Order of pole (three term test) -1126.352423521986 Radius of convergence (six term test) for eq 1 2.2875749326594694 Order of pole (six term test) 0.08503223995034226 TOP MAIN SOLVE Loop x[1] 1.7900000000000007 y[1] (analytic) 1.8922852503083245 y[1] (numeric) 1.8922852503083243 absolute error 2.220446049250313e-16 relative error 1.1734203650789536e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.928835379110416 Order of pole (three term test) -1164.7271745933056 Radius of convergence (six term test) for eq 1 2.3037078085319886 Order of pole (six term test) 0.13229373361995833 TOP MAIN SOLVE Loop x[1] 1.8000000000000007 y[1] (analytic) 1.9022851934029392 y[1] (numeric) 1.902285193402939 absolute error 2.220446049250313e-16 relative error 1.1672519225564836e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 4.039157702494943 Order of pole (three term test) -1200.1120284519332 Radius of convergence (six term test) for eq 1 2.3188680665040766 Order of pole (six term test) 0.17482263422251165 TOP MAIN SOLVE Loop x[1] 1.8100000000000007 y[1] (analytic) 1.912285139811457 y[1] (numeric) 1.9122851398114564 absolute error 6.661338147750939e-16 relative error 3.483443974473241e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 4.137591132438219 Order of pole (three term test) -1232.0364831922361 Radius of convergence (six term test) for eq 1 2.332783253288904 Order of pole (six term test) 0.21010149430265912 TOP MAIN SOLVE Loop x[1] 1.8200000000000007 y[1] (analytic) 1.9222850893408916 y[1] (numeric) 1.922285089340891 absolute error 6.661338147750939e-16 relative error 3.4653226957271787e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 4.222704723123018 Order of pole (three term test) -1260.057688409911 Radius of convergence (six term test) for eq 1 2.3451722616095987 Order of pole (six term test) 0.23551629481880454 TOP MAIN SOLVE Loop x[1] 1.8300000000000007 y[1] (analytic) 1.932285041809496 y[1] (numeric) 1.9322850418094955 absolute error 4.440892098500626e-16 relative error 2.298259315997155e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 4.293215023756053 Order of pole (three term test) -1283.7749729382497 Radius of convergence (six term test) for eq 1 2.3557490152080094 Order of pole (six term test) 0.2484005896661028 TOP MAIN SOLVE Loop x[1] 1.8400000000000007 y[1] (analytic) 1.9422849970461071 y[1] (numeric) 1.9422849970461067 absolute error 4.440892098500626e-16 relative error 2.2864266084814975e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 4.348032006579512 Order of pole (three term test) -1302.8438880414137 Radius of convergence (six term test) for eq 1 2.3642267657764204 Order of pole (six term test) 0.24608850822312966 TOP MAIN SOLVE Loop x[1] 1.8500000000000008 y[1] (analytic) 1.95228495488953 y[1] (numeric) 1.9522849548895294 absolute error 6.661338147750939e-16 relative error 3.412072674671547e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 4.386300138129861 Order of pole (three term test) -1316.9888903099782 Radius of convergence (six term test) for eq 1 2.370322954195309 Order of pole (six term test) 0.22597586887052934 TOP MAIN SOLVE Loop x[1] 1.8600000000000008 y[1] (analytic) 1.9622849151879558 y[1] (numeric) 1.9622849151879551 absolute error 6.661338147750939e-16 relative error 3.394684480420056e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 4.407431797410418 Order of pole (three term test) -1326.013811063763 Radius of convergence (six term test) for eq 1 2.3737645427376988 Order of pole (six term test) 0.18558793256995365 TOP MAIN SOLVE Loop x[1] 1.8700000000000008 y[1] (analytic) 1.9722848777984165 y[1] (numeric) 1.972284877798416 absolute error 4.440892098500626e-16 relative error 2.2516484045944812e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 4.411130636949035 Order of pole (three term test) -1329.809369231239 Radius of convergence (six term test) for eq 1 2.374293676139209 Order of pole (six term test) 0.12265151003166963 TOP MAIN SOLVE Loop x[1] 1.8800000000000008 y[1] (analytic) 1.9822848425862711 y[1] (numeric) 1.9822848425862707 absolute error 4.440892098500626e-16 relative error 2.240289590625447e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 4.3974031527493205 Order of pole (three term test) -1328.3571798068822 Radius of convergence (six term test) for eq 1 2.371673482430104 Order of pole (six term test) 0.03516838878470452 TOP MAIN SOLVE Loop x[1] 1.8900000000000008 y[1] (analytic) 1.9922848094247183 y[1] (numeric) 1.9922848094247174 absolute error 8.881784197001252e-16 relative error 4.4580896039486995e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 4.36655759865967 Order of pole (three term test) -1321.729967511615 Radius of convergence (six term test) for eq 1 2.3656937876209088 Order of pole (six term test) -0.07851355445762209 TOP MAIN SOLVE Loop x[1] 1.9000000000000008 y[1] (analytic) 2.002284778194341 y[1] (numeric) 2.0022847781943396 absolute error 1.3322676295501878e-15 relative error 6.653736991156802e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 4.319190356852051 Order of pole (three term test) -1310.0879875767187 Radius of convergence (six term test) for eq 1 2.3561764850266984 Order of pole (six term test) -0.2196356356785074 TOP MAIN SOLVE Loop x[1] 1.9100000000000008 y[1] (analytic) 2.0122847487826756 y[1] (numeric) 2.0122847487826747 absolute error 8.881784197001252e-16 relative error 4.4137810030982227e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 4.256160832495837 Order of pole (three term test) -1293.6719454897896 Radius of convergence (six term test) for eq 1 2.342980297214067 Order of pole (six term test) -0.38897412067353976 TOP MAIN SOLVE Loop x[1] 1.9200000000000008 y[1] (analytic) 2.022284721083811 y[1] (numeric) 2.0222847210838095 absolute error 1.3322676295501878e-15 relative error 6.587933022785143e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 4.178556774382687 Order of pole (three term test) -1272.7929631446402 Radius of convergence (six term test) for eq 1 2.3260046612085192 Order of pole (six term test) -0.586800394837244 TOP MAIN SOLVE Loop x[1] 1.9300000000000008 y[1] (analytic) 2.032284694998 y[1] (numeric) 2.0322846949979985 absolute error 1.3322676295501878e-15 relative error 6.555516718839921e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 4.087652516228281 Order of pole (three term test) -1247.820323648423 Radius of convergence (six term test) for eq 1 2.3051925312381476 Order of pole (six term test) -0.8128585244645326 TOP MAIN SOLVE Loop x[1] 1.9400000000000008 y[1] (analytic) 2.042284670431306 y[1] (numeric) 2.042284670431305 absolute error 8.881784197001252e-16 relative error 4.348945240393704e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.984862967695454 Order of pole (three term test) -1219.1678362827686 Radius of convergence (six term test) for eq 1 2.2805319099210313 Order of pole (six term test) -1.0663624443704265 TOP MAIN SOLVE Loop x[1] 1.9500000000000008 y[1] (analytic) 2.0522846472952643 y[1] (numeric) 2.052284647295263 absolute error 1.3322676295501878e-15 relative error 6.491631808024304e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.8716962104597163 Order of pole (three term test) -1187.2796786969122 Radius of convergence (six term test) for eq 1 2.2520560178063835 Order of pole (six term test) -1.3460134734961056 TOP MAIN SOLVE Loop x[1] 1.9600000000000009 y[1] (analytic) 2.062284625506559 y[1] (numeric) 2.0622846255065577 absolute error 1.3322676295501878e-15 relative error 6.460154011102822e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.7497073295366268 Order of pole (three term test) -1152.6165134434546 Radius of convergence (six term test) for eq 1 2.2198420829008554 Order of pole (six term test) -1.6500374977479773 TOP MAIN SOLVE Loop x[1] 1.9700000000000009 y[1] (analytic) 2.0722846049867276 y[1] (numeric) 2.0722846049867263 absolute error 1.3322676295501878e-15 relative error 6.428980007592734e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.620455687654596 Order of pole (three term test) -1115.64255418129 Radius of convergence (six term test) for eq 1 2.1840088228668417 Order of pole (six term test) -1.9762397220695753 TOP MAIN SOLVE Loop x[1] 1.9800000000000009 y[1] (analytic) 2.0822845856618772 y[1] (numeric) 2.082284585661876 absolute error 1.3322676295501878e-15 relative error 6.398105420958643e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.485467297405112 Order of pole (three term test) -1076.8140954781807 Radius of convergence (six term test) for eq 1 2.14471276501021 Order of pole (six term test) -2.3220737314828597 TOP MAIN SOLVE Loop x[1] 1.9900000000000009 y[1] (analytic) 2.092284567462417 y[1] (numeric) 2.092284567462416 absolute error 8.881784197001252e-16 relative error 4.2450173055443106e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.3462033519611776 Order of pole (three term test) -1036.5698425504418 Radius of convergence (six term test) for eq 1 2.1021436204974315 Order of pole (six term test) -2.6847206844564333 Finished! diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ; Iterations 90 Total Elapsed Time 0.0 Seconds Elapsed Time(since restart) 0.0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 101.11111111111119%