##############ECHO OF PROBLEM################# ##############temp/sing1postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.000001) /( x * x + 0.000001); ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=-2.0 x_end=-1.5 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=500 $glob_max_h=0.001 ## Not Given = 0 ## No Pole = 3 ## Pole = 4 $glob_type_given_pole=4 ## Real Part $array_given_rad_poles[1][1]=0.0 ## Imag Part $array_given_rad_poles[1][2]=0.001 ## Order $array_given_ord_poles[1][1]=1.0 ## Not Used $array_given_ord_poles[1][2]=0.0 #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(1.0 / (x * x + 0.000001)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 10 desired_abs_gbl_error 1.0e-10 range 0.5 estimated_steps 500000.0 step_error 2.0e-16 est_needed_step_err 2.0e-16 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0057946112143626e-163 estimated_step_error 1.0057946112143626e-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 6.749775127529676e-156 estimated_step_error 6.749775127529676e-156 best_h 4.0e-06 opt_iter 3 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.529699759368462e-148 estimated_step_error 4.529699759368462e-148 best_h 8.0e-06 opt_iter 4 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.039833203538165e-140 estimated_step_error 3.039833203538165e-140 best_h 1.6e-05 opt_iter 5 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.0400017615025516e-132 estimated_step_error 2.0400017615025516e-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 1.369027686663757e-124 estimated_step_error 1.369027686663757e-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 9.187465506037019e-117 estimated_step_error 9.187465506037019e-117 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 6.165706037985222e-109 estimated_step_error 6.165706037985222e-109 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 4.137872599946436e-101 estimated_step_error 4.137872599946436e-101 best_h 0.000512 opt_iter 10 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.777063622068329e-93 estimated_step_error 2.777063622068329e-93 best_h 0.001024 opt_iter 11 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.863903297323973e-85 estimated_step_error 1.863903297323973e-85 best_h 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] -2.0 y[1] (analytic) 0.24999993750001562 y[1] (numeric) 0.24999993750001562 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 2.0000002499999843 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.9000033250219448 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 2.002862593949846 Order of pole (three term test) 677.0401592353243 Radius of convergence (six term test) for eq 1 2.000000188200464 Order of pole (six term test) 1.0000000000410694 TOP MAIN SOLVE Loop x[1] -1.9890000000000012 y[1] (analytic) 0.2527727911323257 y[1] (numeric) 0.2527727911323261 absolute error 3.885780586188048e-16 relative error 1.5372622064191454e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9890002513825897 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.88955334341095 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.9918469547716788 Order of pole (three term test) 677.0401774573537 Radius of convergence (six term test) for eq 1 1.9889993876019798 Order of pole (six term test) 1.00000000064151 TOP MAIN SOLVE Loop x[1] -1.9790000000000023 y[1] (analytic) 0.25533379531727973 y[1] (numeric) 0.25533379531728034 absolute error 6.106226635438361e-16 relative error 2.391468245654954e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9790002526528412 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.880053360305623 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.9818327378453318 Order of pole (three term test) 677.0401942872193 Radius of convergence (six term test) for eq 1 1.9789986591489714 Order of pole (six term test) 1.0000000011480665 TOP MAIN SOLVE Loop x[1] -1.9690000000000034 y[1] (analytic) 0.2579339183618505 y[1] (numeric) 0.2579339183618513 absolute error 8.326672684688674e-16 relative error 3.2282193584976083e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9690002539359952 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.8705533773719107 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.9718185214107342 Order of pole (three term test) 677.0402113741673 Radius of convergence (six term test) for eq 1 1.9689968007511434 Order of pole (six term test) 1.000000002511321 TOP MAIN SOLVE Loop x[1] -1.9590000000000045 y[1] (analytic) 0.26057396105253 y[1] (numeric) 0.26057396105253106 absolute error 1.0547118733938987e-15 relative error 4.0476487717100627e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9590002552322492 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.8610533946124317 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.961804305475426 Order of pole (three term test) 677.0402287234707 Radius of convergence (six term test) for eq 1 1.9589947004274362 Order of pole (six term test) 1.000000004060226 TOP MAIN SOLVE Loop x[1] -1.9490000000000056 y[1] (analytic) 0.26325474477189087 y[1] (numeric) 0.26325474477189226 absolute error 1.3877787807814457e-15 relative error 5.271619252233992e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.949000256541805 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.8515534120298756 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.951790090047047 Order of pole (three term test) 677.0402463405075 Radius of convergence (six term test) for eq 1 1.9489994729755356 Order of pole (six term test) 1.0000000005718999 TOP MAIN SOLVE Loop x[1] -1.9390000000000067 y[1] (analytic) 0.2659771121375445 y[1] (numeric) 0.26597711213754616 absolute error 1.6653345369377348e-15 relative error 6.261194895884658e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9390002578648684 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.8420534296269777 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.9417758751335148 Order of pole (three term test) 677.0402642308417 Radius of convergence (six term test) for eq 1 1.9389998327551634 Order of pole (six term test) 1.0000000003296954 TOP MAIN SOLVE Loop x[1] -1.9290000000000078 y[1] (analytic) 0.26874192766434557 y[1] (numeric) 0.26874192766434757 absolute error 1.9984014443252818e-15 relative error 7.436135707195096e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9290002592016493 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.8325534474065288 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.9317616607427512 Order of pole (three term test) 677.0402824001276 Radius of convergence (six term test) for eq 1 1.9289969918287317 Order of pole (six term test) 1.0000000025806735 TOP MAIN SOLVE Loop x[1] -1.919000000000009 y[1] (analytic) 0.27155007845081514 y[1] (numeric) 0.2715500784508174 absolute error 2.275957200481571e-15 relative error 8.381353500119893e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9190002605523624 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.823053465371386 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.9217474468830513 Order of pole (three term test) 677.0403008542347 Radius of convergence (six term test) for eq 1 1.9189970826068665 Order of pole (six term test) 1.0000000025017517 TOP MAIN SOLVE Loop x[1] -1.90900000000001 y[1] (analytic) 0.27440247489079866 y[1] (numeric) 0.27440247489080116 absolute error 2.4980018054066022e-15 relative error 9.103423015410878e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9090002619172262 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.813553483524458 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.9117332335626689 Order of pole (three term test) 677.0403195991174 Radius of convergence (six term test) for eq 1 1.9089976569456084 Order of pole (six term test) 1.0000000020691306 TOP MAIN SOLVE Loop x[1] -1.8990000000000111 y[1] (analytic) 0.2773000514114263 y[1] (numeric) 0.2773000514114291 absolute error 2.831068712794149e-15 relative error 1.0209405654215807e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8990002632964647 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.8040535018687225 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.9017190207901387 Order of pole (three term test) 677.0403386409183 Radius of convergence (six term test) for eq 1 1.8989997144898394 Order of pole (six term test) 1.0000000004859633 TOP MAIN SOLVE Loop x[1] -1.8890000000000122 y[1] (analytic) 0.2802437672384911 y[1] (numeric) 0.2802437672384942 absolute error 3.1086244689504383e-15 relative error 1.109257308229431e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8890002646903061 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.7945535204072116 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.8917048085741723 Order of pole (three term test) 677.0403579859483 Radius of convergence (six term test) for eq 1 1.8890000520224304 Order of pole (six term test) 1.000000000234019 TOP MAIN SOLVE Loop x[1] -1.8790000000000133 y[1] (analytic) 0.2832346071904163 y[1] (numeric) 0.2832346071904198 absolute error 3.497202527569243e-15 relative error 1.2347370126342302e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8790002660989833 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.7850535391430242 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.8816905969236597 Order of pole (three term test) 677.040377640682 Radius of convergence (six term test) for eq 1 1.8789992777411317 Order of pole (six term test) 1.0000000008561898 TOP MAIN SOLVE Loop x[1] -1.8690000000000144 y[1] (analytic) 0.2862735825020381 y[1] (numeric) 0.28627358250204205 absolute error 3.941291737419306e-15 relative error 1.376757052806731e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8690002675227348 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.7755535580793373 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.871676385847708 Order of pole (three term test) 677.0403976117726 Radius of convergence (six term test) for eq 1 1.8689981428342173 Order of pole (six term test) 1.0000000017664465 TOP MAIN SOLVE Loop x[1] -1.8590000000000155 y[1] (analytic) 0.28936173167949114 y[1] (numeric) 0.2893617316794954 absolute error 4.274358644806853e-15 relative error 1.4771679102132643e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8590002689618035 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.7660535772193806 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.8616621753555018 Order of pole (three term test) 677.040417906016 Radius of convergence (six term test) for eq 1 1.858998914642017 Order of pole (six term test) 1.000000001200556 TOP MAIN SOLVE Loop x[1] -1.8490000000000166 y[1] (analytic) 0.2925001213875451 y[1] (numeric) 0.2925001213875497 absolute error 4.6074255521944e-15 relative error 1.57518756926936e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.849000270416438 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.7565535965664583 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.8516479654565883 Order of pole (three term test) 677.0404385304503 Radius of convergence (six term test) for eq 1 1.8489997411031085 Order of pole (six term test) 1.0000000004547154 TOP MAIN SOLVE Loop x[1] -1.8390000000000177 y[1] (analytic) 0.2956898473708089 y[1] (numeric) 0.2956898473708137 absolute error 4.829470157119431e-15 relative error 1.6332891372705974e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8390002718868927 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.7470536161239492 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.8416337561606522 Order of pole (three term test) 677.0404594922784 Radius of convergence (six term test) for eq 1 1.8389983897552586 Order of pole (six term test) 1.0000000017096404 TOP MAIN SOLVE Loop x[1] -1.8290000000000188 y[1] (analytic) 0.298932035410287 y[1] (numeric) 0.2989320354102923 absolute error 5.2735593669694936e-15 relative error 1.7641332283880128e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8290002733734265 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.737553635895304 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.8316195474775323 Order of pole (three term test) 677.0404807988815 Radius of convergence (six term test) for eq 1 1.8289988832747481 Order of pole (six term test) 1.0000000012698589 TOP MAIN SOLVE Loop x[1] -1.81900000000002 y[1] (analytic) 0.30222784231684785 y[1] (numeric) 0.3022278423168534 absolute error 5.551115123125783e-15 relative error 1.8367318777024312e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8190002748763048 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.7280536558840531 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.8216053394173672 Order of pole (three term test) 677.040502457872 Radius of convergence (six term test) for eq 1 1.8189982838807344 Order of pole (six term test) 1.0000000018779698 TOP MAIN SOLVE Loop x[1] -1.809000000000021 y[1] (analytic) 0.30557845696323976 y[1] (numeric) 0.30557845696324565 absolute error 5.88418203051333e-15 relative error 1.925587977957877e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8090002763957986 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.7185536760937987 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.8115911319905122 Order of pole (three term test) 677.0405244770741 Radius of convergence (six term test) for eq 1 1.8089989306843506 Order of pole (six term test) 1.000000001241803 TOP MAIN SOLVE Loop x[1] -1.7990000000000221 y[1] (analytic) 0.3089851013563752 y[1] (numeric) 0.30898510135638146 absolute error 6.2727600891321345e-15 relative error 2.0301173297987917e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7990002779321852 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.7090536965282297 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.8015769252074867 Order of pole (three term test) 677.0405468645015 Radius of convergence (six term test) for eq 1 1.7989988252054838 Order of pole (six term test) 1.0000000013735022 TOP MAIN SOLVE Loop x[1] -1.7890000000000232 y[1] (analytic) 0.31244903175168737 y[1] (numeric) 0.31244903175169403 absolute error 6.661338147750939e-15 relative error 2.1319759291316686e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7890002794857478 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.699553717191109 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.7915627190791046 Order of pole (three term test) 677.0405696284195 Radius of convergence (six term test) for eq 1 1.7889995969459733 Order of pole (six term test) 1.0000000007070735 TOP MAIN SOLVE Loop x[1] -1.7790000000000243 y[1] (analytic) 0.3159715398114574 y[1] (numeric) 0.3159715398114645 absolute error 7.049916206369744e-15 relative error 2.2311870906400247e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7790002810567755 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.6900537380862934 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.7815485136164035 Order of pole (three term test) 677.040592777315 Radius of convergence (six term test) for eq 1 1.7789990172019254 Order of pole (six term test) 1.0000000012594121 TOP MAIN SOLVE Loop x[1] -1.7690000000000254 y[1] (analytic) 0.3195539538091059 y[1] (numeric) 0.3195539538091132 absolute error 7.327471962526033e-15 relative error 2.293031231559505e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7690002826455653 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.6805537592177175 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.7715343088307176 Order of pole (three term test) 677.040616319937 Radius of convergence (six term test) for eq 1 1.7689989524609713 Order of pole (six term test) 1.0000000013390036 TOP MAIN SOLVE Loop x[1] -1.7590000000000265 y[1] (analytic) 0.32319763988154476 y[1] (numeric) 0.32319763988155253 absolute error 7.771561172376096e-15 relative error 2.4045847535348503e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7590002842524197 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.6710537805894177 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.7615201047335036 Order of pole (three term test) 677.0406402652274 Radius of convergence (six term test) for eq 1 1.7589986076263546 Order of pole (six term test) 1.0000000017549002 TOP MAIN SOLVE Loop x[1] -1.7490000000000276 y[1] (analytic) 0.32690400333179526 y[1] (numeric) 0.3269040033318035 absolute error 8.271161533457416e-15 relative error 2.5301499673170104e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7490002858776488 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.6615538022055105 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.7515059013366492 Order of pole (three term test) 677.040664622452 Radius of convergence (six term test) for eq 1 1.7490018246438845 Order of pole (six term test) 0.9999999984365839 TOP MAIN SOLVE Loop x[1] -1.7390000000000287 y[1] (analytic) 0.3306744899841894 y[1] (numeric) 0.3306744899841981 absolute error 8.659739592076221e-15 relative error 2.6188109014669595e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.739000287521569 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.652053824070214 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.7414916986522255 Order of pole (three term test) 677.0406894011105 Radius of convergence (six term test) for eq 1 1.7390007910038985 Order of pole (six term test) 0.9999999994779678 TOP MAIN SOLVE Loop x[1] -1.7290000000000298 y[1] (analytic) 0.3345105875945964 y[1] (numeric) 0.3345105875946054 absolute error 8.992806499463768e-15 relative error 2.6883473447370896e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7290002891845053 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.6425538461878428 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.7314774966926059 Order of pole (three term test) 677.0407146109844 Radius of convergence (six term test) for eq 1 1.7289992656828668 Order of pole (six term test) 1.000000001090731 TOP MAIN SOLVE Loop x[1] -1.719000000000031 y[1] (analytic) 0.33841382731824093 y[1] (numeric) 0.3384138273182504 absolute error 9.492406860545088e-15 relative error 2.804970156145105e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7190002908667894 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.6330538685628055 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.7214632954703764 Order of pole (three term test) 677.040740262115 Radius of convergence (six term test) for eq 1 1.7190007251316506 Order of pole (six term test) 0.9999999994998507 TOP MAIN SOLVE Loop x[1] -1.709000000000032 y[1] (analytic) 0.3423857852378186 y[1] (numeric) 0.3423857852378284 absolute error 9.825473767932635e-15 relative error 2.86970843754741e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7090002925687606 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.6235538911996248 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.7114490949985486 Order of pole (three term test) 677.0407663648849 Radius of convergence (six term test) for eq 1 1.7089997538466501 Order of pole (six term test) 1.0000000005982805 TOP MAIN SOLVE Loop x[1] -1.6990000000000332 y[1] (analytic) 0.34642808395475405 y[1] (numeric) 0.3464280839547644 absolute error 1.0325074129013956e-14 relative error 2.9804379630961107e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.699000294290767 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.6140539141029266 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.7014348952903315 Order of pole (three term test) 677.0407929299404 Radius of convergence (six term test) for eq 1 1.6989994034183327 Order of pole (six term test) 1.0000000010324221 TOP MAIN SOLVE Loop x[1] -1.6890000000000343 y[1] (analytic) 0.35054239424660355 y[1] (numeric) 0.3505423942466144 absolute error 1.0824674490095276e-14 relative error 3.087978706073483e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.689000296033164 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.6045539372774416 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.6914206963593539 Order of pole (three term test) 677.0408199682903 Radius of convergence (six term test) for eq 1 1.6889965706186807 Order of pole (six term test) 1.0000000042775152 TOP MAIN SOLVE Loop x[1] -1.6790000000000354 y[1] (analytic) 0.35473043679376104 y[1] (numeric) 0.3547304367937723 absolute error 1.1268763699945339e-14 relative error 3.176711815822265e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.6790002977963163 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.5950539607280154 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.6814064982194543 Order of pole (three term test) 677.0408474912247 Radius of convergence (six term test) for eq 1 1.6789966911000445 Order of pole (six term test) 1.0000000041666137 TOP MAIN SOLVE Loop x[1] -1.6690000000000365 y[1] (analytic) 0.3589939839788008 y[1] (numeric) 0.35899398397881255 absolute error 1.176836406102666e-14 relative error 3.2781507730562978e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.6690002995805968 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.5855539844596056 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.6713923008848113 Order of pole (three term test) 677.0408755103775 Radius of convergence (six term test) for eq 1 1.668999515995928 Order of pole (six term test) 1.0000000009327046 TOP MAIN SOLVE Loop x[1] -1.6590000000000376 y[1] (analytic) 0.36333486176196866 y[1] (numeric) 0.363334861761981 absolute error 1.2323475573339238e-14 relative error 3.3917679997942803e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.6590003013863877 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.5760540084773043 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.6613781043700828 Order of pole (three term test) 677.0409040377835 Radius of convergence (six term test) for eq 1 1.6589990641373236 Order of pole (six term test) 1.0000000014617694 TOP MAIN SOLVE Loop x[1] -1.6490000000000387 y[1] (analytic) 0.36775495163652905 y[1] (numeric) 0.3677549516365419 absolute error 1.2878587085651816e-14 relative error 3.5019479760480234e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.6490003032140799 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.5665540327863097 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.651363908690157 Order of pole (three term test) 677.040933085801 Radius of convergence (six term test) for eq 1 1.6489987573075955 Order of pole (six term test) 1.0000000019009239 TOP MAIN SOLVE Loop x[1] -1.6390000000000398 y[1] (analytic) 0.372256192667875 y[1] (numeric) 0.3722561926678884 absolute error 1.3378187446733136e-14 relative error 3.59381192582848e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.639000305064075 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.5570540573919578 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.6413497138602808 Order of pole (three term test) 677.0409626671587 Radius of convergence (six term test) for eq 1 1.6390001316987861 Order of pole (six term test) 1.0000000002370513 TOP MAIN SOLVE Loop x[1] -1.6290000000000409 y[1] (analytic) 0.37684058362052975 y[1] (numeric) 0.37684058362054373 absolute error 1.3988810110276972e-14 relative error 3.712129403865747e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.629000306936783 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.5475540822997076 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.6313355198961377 Order of pole (three term test) 677.0409927950068 Radius of convergence (six term test) for eq 1 1.6289989226050892 Order of pole (six term test) 1.0000000018066277 TOP MAIN SOLVE Loop x[1] -1.619000000000042 y[1] (analytic) 0.3815101851773939 y[1] (numeric) 0.38151018517740837 absolute error 1.4488410471358293e-14 relative error 3.797647096792842e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.6190003088326252 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.5380541075151584 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.6213213268137872 Order of pole (three term test) 677.0410234828971 Radius of convergence (six term test) for eq 1 1.6189985130330766 Order of pole (six term test) 1.0000000023486333 TOP MAIN SOLVE Loop x[1] -1.609000000000043 y[1] (analytic) 0.3862671222558411 y[1] (numeric) 0.3862671222558561 absolute error 1.4988010832439613e-14 relative error 3.8802191459910014e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.609000310752033 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.528554133044052 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.6113071346296406 Order of pole (three term test) 677.0410547447799 Radius of convergence (six term test) for eq 1 1.6089993940969274 Order of pole (six term test) 1.000000001245759 TOP MAIN SOLVE Loop x[1] -1.5990000000000442 y[1] (analytic) 0.3911135864255209 y[1] (numeric) 0.39111358642553645 absolute error 1.554312234475219e-14 relative error 3.974068629730929e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.5990003126954484 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.5190541588922657 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.601292943360593 Order of pole (three term test) 677.0410865950793 Radius of convergence (six term test) for eq 1 1.5989992903277408 Order of pole (six term test) 1.0000000014181385 TOP MAIN SOLVE Loop x[1] -1.5890000000000453 y[1] (analytic) 0.39605183843300623 y[1] (numeric) 0.39605183843302233 absolute error 1.609823385706477e-14 relative error 4.064678482685001e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.5890003146633245 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.5095541850658278 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.5912787530238706 Order of pole (three term test) 677.0411190486335 Radius of convergence (six term test) for eq 1 1.5889995835664004 Order of pole (six term test) 1.0000000010947883 TOP MAIN SOLVE Loop x[1] -1.5790000000000464 y[1] (analytic) 0.4010842108387157 y[1] (numeric) 0.4010842108387323 absolute error 1.659783421814609e-14 relative error 4.138241738172143e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.5790003166561262 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.500054211570922 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.5812645636372353 Order of pole (three term test) 677.0411521207931 Radius of convergence (six term test) for eq 1 1.5789984849341736 Order of pole (six term test) 1.0000000025818245 TOP MAIN SOLVE Loop x[1] -1.5690000000000475 y[1] (analytic) 0.40621311077185346 y[1] (numeric) 0.40621311077187056 absolute error 1.709743457922741e-14 relative error 4.208981474463057e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.56900031867433 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.490554238413884 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.5712503752188418 Order of pole (three term test) 677.0411858273745 Radius of convergence (six term test) for eq 1 1.5689992897459923 Order of pole (six term test) 1.0000000014923973 TOP MAIN SOLVE Loop x[1] -1.5590000000000486 y[1] (analytic) 0.4114410228094418 y[1] (numeric) 0.4114410228094595 absolute error 1.7708057242771247e-14 relative error 4.3039114383527824e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.5590003207184249 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.4810542656012213 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.5612361877873242 Order of pole (three term test) 677.0412201847075 Radius of convergence (six term test) for eq 1 1.559000312426389 Order of pole (six term test) 0.9999999999934879 TOP MAIN SOLVE Loop x[1] -1.5490000000000497 y[1] (analytic) 0.41677051198587645 y[1] (numeric) 0.4167705119858947 absolute error 1.8263168755083825e-14 relative error 4.382068363728845e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.5490003227889122 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.4715542931396008 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.5512220013618037 Order of pole (three term test) 677.0412552096549 Radius of convergence (six term test) for eq 1 1.5490006586897704 Order of pole (six term test) 0.9999999994675761 TOP MAIN SOLVE Loop x[1] -1.5390000000000508 y[1] (analytic) 0.4222042269398106 y[1] (numeric) 0.4222042269398294 absolute error 1.8818280267396403e-14 relative error 4.45715108154972e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.5390003248863062 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.4620543210358659 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.5412078159618645 Order of pole (three term test) 677.0412909196143 Radius of convergence (six term test) for eq 1 1.5389990337925605 Order of pole (six term test) 1.0000000019743567 TOP MAIN SOLVE Loop x[1] -1.5290000000000519 y[1] (analytic) 0.4277449032055768 y[1] (numeric) 0.4277449032055962 absolute error 1.942890293094024e-14 relative error 4.542170528587828e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.5290003270111354 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.452554349297039 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.5311936316076997 Order of pole (three term test) 677.0413273325963 Radius of convergence (six term test) for eq 1 1.5290000205630945 Order of pole (six term test) 1.0000000004704628 TOP MAIN SOLVE Loop x[1] -1.519000000000053 y[1] (analytic) 0.4333953666567839 y[1] (numeric) 0.43339536665680395 absolute error 2.0039525594484076e-14 relative error 4.623843985474319e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.519000329163941 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.4430543779303249 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.5211794483198604 Order of pole (three term test) 677.0413644671304 Radius of convergence (six term test) for eq 1 1.5190001918065206 Order of pole (six term test) 1.0000000002797425 TOP MAIN SOLVE Loop x[1] -1.509000000000054 y[1] (analytic) 0.4391585371101823 y[1] (numeric) 0.4391585371102031 absolute error 2.0761170560490427e-14 relative error 4.727488778222606e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.5090003313452796 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.4335544069431263 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.5111652661196702 Order of pole (three term test) 677.0414023424594 Radius of convergence (six term test) for eq 1 1.5089989742938323 Order of pole (six term test) 1.0000000021984956 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.000001) /( x * x + 0.000001); Iterations 501 Total Elapsed Time 1.0 Seconds Elapsed Time(since restart) 1.0 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.39999999998895%