##############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=1.4 x_end=2.1 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=1000000 $glob_max_h=0.0001 # 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=1000000000 $glob_max_minutes=30.0 $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 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-10 range 0.7000000000000002 estimated_steps 700000.0000000002 step_error 1.428571428571428e-16 est_needed_step_err 1.428571428571428e-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 3.761030142203954e-162 estimated_step_error 3.761030142203954e-162 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 2.523983830929007e-154 estimated_step_error 2.523983830929007e-154 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 1.6938158400495767e-146 estimated_step_error 1.6938158400495767e-146 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 1.1366991774383315e-138 estimated_step_error 1.1366991774383315e-138 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 7.628240380191778e-131 estimated_step_error 7.628240380191778e-131 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 5.1192004033047463e-123 estimated_step_error 5.1192004033047463e-123 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 3.4354036033728477e-115 estimated_step_error 3.4354036033728477e-115 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 2.3054151916901443e-107 estimated_step_error 2.3054151916901443e-107 best_h 0.0001 START of Soultion TOP MAIN SOLVE Loop x[1] 1.4 y[1] (analytic) -2.514161640922489 y[1] (numeric) -2.514161640922489 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6250479763430041 Order of pole (three term test) 0.8487445406934904 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4100999999999988 y[1] (analytic) -2.476766516712337 y[1] (numeric) -2.476761735525513 absolute error 4.78118682378792e-06 relative error 0.00019304148338271599% Correct digits 6 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6385011158092015 Order of pole (three term test) 0.8473113850384826 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4200999999999977 y[1] (analytic) -2.440767761672973 y[1] (numeric) -2.4407584574392 absolute error 9.304233772766679e-06 relative error 0.00038120110888343136% Correct digits 6 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6517637515179215 Order of pole (three term test) 0.8458840258526014 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4300999999999966 y[1] (analytic) -2.405746059246014 y[1] (numeric) -2.4057324295606177 absolute error 1.3629685396310265e-05 relative error 0.0005665471359259734% Correct digits 6 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.664970806916984 Order of pole (three term test) 0.8444469434911963 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4400999999999955 y[1] (analytic) -2.3716600771253558 y[1] (numeric) -2.3716423083283997 absolute error 1.7768796956030286e-05 relative error 0.0007492134782471655% Correct digits 6 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6781236634949286 Order of pole (three term test) 0.8429989267528282 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4500999999999944 y[1] (analytic) -2.3384707879142534 y[1] (numeric) -2.3384490558779256 absolute error 2.1732036327826165e-05 relative error 0.0009293268250406313% Correct digits 6 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6912236527122022 Order of pole (three term test) 0.8415389043018742 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4600999999999933 y[1] (analytic) -2.3061413105158777 y[1] (numeric) -2.306115781366851 absolute error 2.5529149026759512e-05 relative error 0.0011070071426390047% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7042720583872695 Order of pole (three term test) 0.840065930863777 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4700999999999922 y[1] (analytic) -2.27463676444596 y[1] (numeric) -2.274607595228883 absolute error 2.916921707685205e-05 relative error 0.0012823681359936554% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7172701189575905 Order of pole (three term test) 0.8385791750554598 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.480099999999991 y[1] (analytic) -2.243924135855697 y[1] (numeric) -2.2438914751433408 absolute error 3.266071235641377e-05 relative error 0.0014555176725686827% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7302190296209752 Order of pole (three term test) 0.8370779086207183 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.49009999999999 y[1] (analytic) -2.2139721541812123 y[1] (numeric) -2.2139361426361917 absolute error 3.601154502064219e-05 relative error 0.0016265581729486677% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7431199443629068 Order of pole (three term test) 0.8355614968828392 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5000999999999889 y[1] (analytic) -2.1847511784490146 y[1] (numeric) -2.1847119493415232 absolute error 3.9229107491323134e-05 relative error 0.0017955869701909224% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7559739778756172 Order of pole (three term test) 0.8340293902542808 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5100999999999878 y[1] (analytic) -2.1562330923669064 y[1] (numeric) -2.1561907720523865 absolute error 4.232031451989471e-05 relative error 0.0019626966430349845% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7687822073742083 Order of pole (three term test) 0.832481116661933 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5200999999999867 y[1] (analytic) -2.128391207418326 y[1] (numeric) -2.1283459157786857 absolute error 4.5291639640510084e-05 relative error 0.0021279753215785674% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7815456743151452 Order of pole (three term test) 0.8309162747675012 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5300999999999856 y[1] (analytic) -2.1012001732566787 y[1] (numeric) -2.101152024108219 absolute error 4.814914845985285e-05 relative error 0.002291506971714448% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7942653860226299 Order of pole (three term test) 0.8293345278905057 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5400999999999845 y[1] (analytic) -2.0746358947660246 y[1] (numeric) -2.07458499623698 absolute error 5.089852904482939e-05 relative error 0.002453371657804546% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.806942317227213 Order of pole (three term test) 0.827735598532246 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5500999999999834 y[1] (analytic) -2.0486754552165025 y[1] (numeric) -2.048621910096807 absolute error 5.354511969546394e-05 relative error 0.002613645785579314% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.819577411521899 Order of pole (three term test) 0.826119263438058 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5600999999999823 y[1] (analytic) -2.023297044998317 y[1] (numeric) -2.02324095106393 absolute error 5.609393438676946e-05 relative error 0.002772402328438933% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8321715827401406 Order of pole (three term test) 0.8244853491263128 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5700999999999812 y[1] (analytic) -1.9984798954673721 y[1] (numeric) -1.998421345781308 absolute error 5.854968606411326e-05 relative error 0.002929711036718766% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8447257162600965 Order of pole (three term test) 0.8228337278312972 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.58009999999998 y[1] (analytic) -1.9742042174798464 y[1] (numeric) -1.9741433006718223 absolute error 6.091680802411403e-05 relative error 0.003085638632758918% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8572406702390558 Order of pole (three term test) 0.8211643138077735 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.590099999999979 y[1] (analytic) -1.9504511442324655 y[1] (numeric) -1.9503879447589179 absolute error 6.31994735476038e-05 relative error 0.003240248992367037% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8697172767826113 Order of pole (three term test) 0.8194770599640511 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6000999999999779 y[1] (analytic) -1.9272026780605926 y[1] (numeric) -1.927137276446657 absolute error 6.540161393564503e-05 relative error 0.0033936033132467842% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8821563430513584 Order of pole (three term test) 0.8177719547741784 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6100999999999768 y[1] (analytic) -1.9044416408780471 y[1] (numeric) -1.9043741139429362 absolute error 6.752693511091756e-05 relative error 0.0035457602722750864% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8945586523095352 Order of pole (three term test) 0.8160490194517406 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6200999999999757 y[1] (analytic) -1.882151627971078 y[1] (numeric) -1.8820820490381682 absolute error 6.957893290970851e-05 relative error 0.003696776172316851% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9069249649183135 Order of pole (three term test) 0.8143083053463466 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6300999999999746 y[1] (analytic) -1.8603169648845705 y[1] (numeric) -1.8602454039773857 absolute error 7.15609071848533e-05 relative error 0.0038467050795988164% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.919256019277433 Order of pole (three term test) 0.812549891548732 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6400999999999735 y[1] (analytic) -1.8389226671616796 y[1] (numeric) -1.8388491911868845 absolute error 7.347597479512302e-05 relative error 0.003995598950799324% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9315525327176528 Order of pole (three term test) 0.8107738826755815 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6500999999999724 y[1] (analytic) -1.81795440271898 y[1] (numeric) -1.8178790756373462 absolute error 7.532708163382473e-05 relative error 0.004143507753613819% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9438152023471924 Order of pole (three term test) 0.8089804068221939 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6600999999999713 y[1] (analytic) -1.7973984566579462 y[1] (numeric) -1.7973213396442305 absolute error 7.711701371571067e-05 relative error 0.004290479577861706% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9560447058545816 Order of pole (three term test) 0.8071696136605374 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6700999999999702 y[1] (analytic) -1.7772416983307036 y[1] (numeric) -1.7771628499232335 absolute error 7.884840747007793e-05 relative error 0.004436560741520823% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.968241702270744 Order of pole (three term test) 0.8053416726780063 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.680099999999969 y[1] (analytic) -1.7574715504932843 y[1] (numeric) -1.7573910267340493 absolute error 8.05237592349517e-05 relative error 0.004581795888095624% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9804068326921116 Order of pole (three term test) 0.8034967715332756 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.690099999999968 y[1] (analytic) -1.738075960393635 y[1] (numeric) -1.7379938149595509 absolute error 8.214543408424646e-05 relative error 0.004726228079562321% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.992540720967627 Order of pole (three term test) 0.8016351145279421 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7000999999999669 y[1] (analytic) -1.7190433726542311 y[1] (numeric) -1.7189596569802392 absolute error 8.371567399190205e-05 relative error 0.004869898882344293% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0046439743514908 Order of pole (three term test) 0.7997569211824963 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7100999999999658 y[1] (analytic) -1.700362703820664 y[1] (numeric) -1.700277467215229 absolute error 8.523660543491296e-05 relative error 0.005012848449533083% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0167171841230105 Order of pole (three term test) 0.7978624248988544 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7200999999999647 y[1] (analytic) -1.6820233184579663 y[1] (numeric) -1.6819366082115381 absolute error 8.671024642814551e-05 relative error 0.005155115596592271% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0287609261765507 Order of pole (three term test) 0.7959518717169063 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7300999999999636 y[1] (analytic) -1.6640150066859716 y[1] (numeric) -1.6639268681728796 absolute error 8.813851309197318e-05 relative error 0.005296737874227984% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0407757615825064 Order of pole (three term test) 0.794025519148655 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7400999999999625 y[1] (analytic) -1.6463279630536054 y[1] (numeric) -1.6462384398278682 absolute error 8.952322573718696e-05 relative error 0.005437751635533146% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.052762237120963 Order of pole (three term test) 0.7920836350842 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7500999999999614 y[1] (analytic) -1.6289527666599204 y[1] (numeric) -1.6288619005453706 absolute error 9.086611454978133e-05 relative error 0.005578192100443611% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.064720885789985 Order of pole (three term test) 0.7901264967684805 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7600999999999603 y[1] (analytic) -1.6118803624368465 y[1] (numeric) -1.6117881936119705 absolute error 9.216882487605993e-05 relative error 0.005718093415861136% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0766522272895402 Order of pole (three term test) 0.7881543898389439 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7700999999999592 y[1] (analytic) -1.5951020435151955 y[1] (numeric) -1.5950086105930414 absolute error 9.343292215402421e-05 relative error 0.005857488712641985% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0885567684830026 Order of pole (three term test) 0.7861676074276766 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.780099999999958 y[1] (analytic) -1.5786094346014787 y[1] (numeric) -1.5785147747049686 absolute error 9.465989651014084e-05 relative error 0.005996410159175174% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.100435003836483 Order of pole (three term test) 0.7841664493102737 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.790099999999957 y[1] (analytic) -1.5623944762985542 y[1] (numeric) -1.5622986251314939 absolute error 9.585116706034569e-05 relative error 0.00613488901262793% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1122874158385145 Order of pole (three term test) 0.7821512211148541 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8000999999999558 y[1] (analytic) -1.5464494103081523 y[1] (numeric) -1.546352402222235 absolute error 9.700808591728283e-05 relative error 0.0062729556667458376% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.124114475400169 Order of pole (three term test) 0.7801222335742735 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8100999999999547 y[1] (analytic) -1.5307667654579464 y[1] (numeric) -1.5306686335160042 absolute error 9.813194194219221e-05 relative error 0.006410639697474417% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1359166422371634 Order of pole (three term test) 0.7780798018270081 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8200999999999536 y[1] (analytic) -1.515339344500045 y[1] (numeric) -1.515240120535787 absolute error 9.922396425787738e-05 relative error 0.006547969906411576% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1476943652347114 Order of pole (three term test) 0.776024244756872 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8300999999999525 y[1] (analytic) -1.5001602116316473 y[1] (numeric) -1.500059926306127 absolute error 0.00010028532552031066 relative error 0.006684974360920789% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.159448082796271 Order of pole (three term test) 0.7739558843761867 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8400999999999514 y[1] (analytic) -1.4852226806922073 y[1] (numeric) -1.485121363547199 absolute error 0.00010131714500838385 relative error 0.006821680433883737% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.17117822317712 Order of pole (three term test) 0.771875045246953 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8500999999999503 y[1] (analytic) -1.4705203039946546 y[1] (numeric) -1.470417983503157 absolute error 0.00010232049149760947 relative error 0.006958114840009812% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1828852048030805 Order of pole (three term test) 0.7697820539344603 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8600999999999492 y[1] (analytic) -1.4560468617513147 y[1] (numeric) -1.455943565365347 absolute error 0.00010329638596773272 relative error 0.007094303671208022% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.19456943657591 Order of pole (three term test) 0.767677238498813 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8700999999999481 y[1] (analytic) -1.4417963520578636 y[1] (numeric) -1.4416921062537325 absolute error 0.00010424580413115336 relative error 0.007230272429415168% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.206231318165523 Order of pole (three term test) 0.7655609280156722 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.880099999999947 y[1] (analytic) -1.4277629814012804 y[1] (numeric) -1.4276578117224612 absolute error 0.00010516967881923911 relative error 0.00736604605871068% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2178712402898184 Order of pole (three term test) 0.7634334521268563 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.890099999999946 y[1] (analytic) -1.4139411556600687 y[1] (numeric) -1.413835086757847 absolute error 0.00010606890222164544 relative error 0.007501648975775757% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2294895849831318 Order of pole (three term test) 0.7612951406213717 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9000999999999448 y[1] (analytic) -1.400325471567198 y[1] (numeric) -1.4002185272392234 absolute error 0.00010694432797464515 relative error 0.007637105097785345% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2410867258537017 Order of pole (three term test) 0.759146323044983 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9100999999999437 y[1] (analytic) -1.3869107086082684 y[1] (numeric) -1.3868029118351148 absolute error 0.00010779677315353453 relative error 0.007772437871051267% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2526630283301405 Order of pole (three term test) 0.7569873283285554 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9200999999999426 y[1] (analytic) -1.373691821329184 y[1] (numeric) -1.3735831943090653 absolute error 0.00010862702011871228 relative error 0.007907670296355467% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2642188498987523 Order of pole (three term test) 0.7548184844500914 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9300999999999415 y[1] (analytic) -1.3606639320294123 y[1] (numeric) -1.360554496211141 absolute error 0.00010943581827116411 relative error 0.008042824954428096% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.275754540330771 Order of pole (three term test) 0.7526401181114074 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9400999999999404 y[1] (analytic) -1.3478223238184441 y[1] (numeric) -1.3477120999327468 absolute error 0.00011022388569736918 relative error 0.008177924029711849% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2872704419011956 Order of pole (three term test) 0.7504525544430919 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9500999999999393 y[1] (analytic) -1.3351624340145598 y[1] (numeric) -1.335051442103834 absolute error 0.00011099191072583281 relative error 0.008312989333597627% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2987668895989644 Order of pole (three term test) 0.7482561167279356 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9600999999999382 y[1] (analytic) -1.3226798478663726 y[1] (numeric) -1.3225681073129831 absolute error 0.0001117405533894722 relative error 0.008448042326321214% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.310244211328705 Order of pole (three term test) 0.7460511261403522 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9700999999999371 y[1] (analytic) -1.310370292578865 y[1] (numeric) -1.3102578221320602 absolute error 0.0001124704468047355 relative error 0.008583104137944766% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3217027281055667 Order of pole (three term test) 0.7438379015114932 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.980099999999936 y[1] (analytic) -1.298229631626845 y[1] (numeric) -1.2981164494283668 absolute error 0.00011318219847811228 relative error 0.008718195588886748% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.333142754242298 Order of pole (three term test) 0.7416167591077584 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.990099999999935 y[1] (analytic) -1.286253859339782 y[1] (numeric) -1.2861399829482534 absolute error 0.0001138763915287111 relative error 0.00885333720881214% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3445645975293297 Order of pole (three term test) 0.7393880124258754 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.000099999999934 y[1] (analytic) -1.2744390957430538 y[1] (numeric) -1.274324542157194 absolute error 0.00011455358585976683 relative error 0.008988549256092703% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3559685594087063 Order of pole (three term test) 0.7371519720061719 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.010099999999955 y[1] (analytic) -1.2627815816414987 y[1] (numeric) -1.2626663673222756 absolute error 0.00011521431922312253 relative error 0.009123851733199547% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.367354935141346 Order of pole (three term test) 0.7349089452597608 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0200999999999762 y[1] (analytic) -1.251277673932233 y[1] (numeric) -1.2511618148238937 absolute error 0.00011585910833944446 relative error 0.009259264410540357% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.378724013968474 Order of pole (three term test) 0.7326592363095576 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0300999999999974 y[1] (analytic) -1.2399238411340958 y[1] (numeric) -1.239807352684296 absolute error 0.00011648844979972317 relative error 0.00939480683694065% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3900760792675873 Order of pole (three term test) 0.7304031458472119 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0400000000000182 y[1] (analytic) -1.2288280160087433 y[1] (numeric) -1.228710919258855 absolute error 0.00011709674988824581 relative error 0.009529140641550336% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.401298137352772 Order of pole (three term test) 0.7281636218990716 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0500000000000393 y[1] (analytic) -1.2177627467532839 y[1] (numeric) -1.2176450500004004 absolute error 0.00011769675288353376 relative error 0.009664998637651615% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.412617166327841 Order of pole (three term test) 0.7258957125783934 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0600000000000604 y[1] (analytic) -1.2068376177387048 y[1] (numeric) -1.2067193350566214 absolute error 0.00011828268208335935 relative error 0.00980104368183268% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.4239199955616626 Order of pole (three term test) 0.7236222990920887 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0700000000000816 y[1] (analytic) -1.19604950227078 y[1] (numeric) -1.1959306473081457 absolute error 0.00011885496263430717 relative error 0.009937294602660933% Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.4352068864813123 Order of pole (three term test) 0.721343667242637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0800000000001027 y[1] (analytic) -1.1853953658283813 y[1] (numeric) -1.1852759518246325 absolute error 0.00011941400374881894 relative error 0.010073770084748872% Correct digits 4 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.4464780953512193 Order of pole (three term test) 0.7190600988594734 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0900000000001238 y[1] (analytic) -1.174872262671408 y[1] (numeric) -1.1747523024719932 absolute error 0.00011996019941484803 relative error 0.010210488682581051% Correct digits 4 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.4577338733998713 Order of pole (three term test) 0.7167718717227258 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 7000 Total Elapsed Time 27 Seconds Elapsed Time(since restart) 27 Seconds Time to Timeout 29 Minutes 33.0 Seconds Percent Done 100.01428571430642%