##############ECHO OF PROBLEM################# ##############temp/mtest7postode.ode################# diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * y2 ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.0 x_end=0.5 ## ## Trouble about Pi/4??? ## $array_y1_init[0 + 1] = exact_soln_y1(x_start) $array_y2_init[0 + 1] = exact_soln_y2(x_start) $array_y2_init[1 + 1] = exact_soln_y2p(x_start) $array_y2_init[2 + 1] = exact_soln_y2pp(x_start) $array_y2_init[4 + 1] = exact_soln_y2pppp(x_start) $glob_look_poles=true $glob_max_iter=20 $glob_max_h=0.001 #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_y1 (x) return( cos(x)) end def exact_soln_y2 (x) return( sin(x)) end def exact_soln_y2p (x) return( cos(x)) end def exact_soln_y2pp (x) return( -sin(x)) end def exact_soln_y2ppp (x) return( -cos(x)) end def exact_soln_y2pppp (x) return( sin(x)) 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 2.4795962632247947e-183 estimated_step_error 2.4795962632247947e-183 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 1.6640288840366095e-175 estimated_step_error 1.6640288840366095e-175 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 1.116710880708846e-167 estimated_step_error 1.116710880708846e-167 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 7.494119862081017e-160 estimated_step_error 7.494119862081017e-160 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 5.029218706240937e-152 estimated_step_error 5.029218706240937e-152 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 3.37505154183379e-144 estimated_step_error 3.37505154183379e-144 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 2.2649587491391413e-136 estimated_step_error 2.2649587491391413e-136 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 1.5199880866158875e-128 estimated_step_error 1.5199880866158875e-128 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 1.0200467378632581e-120 estimated_step_error 1.0200467378632581e-120 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 6.845417780490904e-113 estimated_step_error 6.845417780490904e-113 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 4.593882108541459e-105 estimated_step_error 4.593882108541459e-105 best_h 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y2[1] (analytic) 0.0 y2[1] (numeric) 0.0 absolute error 0.0 relative error -1.0% Correct digits -1 h 0.001 y1[1] (analytic) 1.0 y1[1] (numeric) 1.0 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.010000000000000002 y2[1] (analytic) 0.009999833334166666 y2[1] (numeric) 0.010000000000833334 absolute error 1.666666666674116e-07 relative error 0.001666694444775971% Correct digits 5 h 0.001 y1[1] (analytic) 0.9999500004166653 y1[1] (numeric) 0.9999499999999987 absolute error 4.166665901195188e-10 relative error 4.166874243171155e-08% Correct digits 10 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.010000368432921592 Order of pole (six term test) -9.500000000333337 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.02000000000000001 y2[1] (analytic) 0.01999866669333309 y2[1] (numeric) 0.020000000026666423 absolute error 1.3333333333323538e-06 relative error 0.006667111131847825% Correct digits 5 h 0.001 y1[1] (analytic) 0.9998000066665778 y1[1] (numeric) 0.9997999999999112 absolute error 6.666666552135325e-09 relative error 6.668000107704125e-07% Correct digits 9 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.020002800681025425 Order of pole (six term test) -9.500000005333565 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.03000000000000002 y2[1] (analytic) 0.02999550020249568 y2[1] (numeric) 0.03000000020249568 absolute error 4.4999999999975615e-06 relative error 0.015002250236264282% Correct digits 4 h 0.001 y1[1] (analytic) 0.9995500337489875 y1[1] (numeric) 0.9995499999989877 absolute error 3.3749999794885355e-08 relative error 3.376519299219076e-06% Correct digits 8 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.0300094467598454 Order of pole (six term test) -9.500000027002631 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.04000000000000003 y2[1] (analytic) 0.03998933418663419 y2[1] (numeric) 0.040000000853300854 absolute error 1.066666666666577e-05 relative error 0.026673779105406904% Correct digits 4 h 0.001 y1[1] (analytic) 0.9992001066609779 y1[1] (numeric) 0.9991999999943115 absolute error 1.0666666638847744e-07 relative error 1.067520566475167e-05% Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.04002239191770079 Order of pole (six term test) -9.500000085348123 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.05000000000000004 y2[1] (analytic) 0.049979169270678366 y2[1] (numeric) 0.05000000260401169 absolute error 2.08333333333241e-05 relative error 0.04168403284275183% Correct digits 4 h 0.001 y1[1] (analytic) 0.9987502603949663 y1[1] (numeric) 0.9987499999782997 absolute error 2.604166665642893e-07 relative error 2.607425268267813e-05% Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.05004372423322657 Order of pole (six term test) -9.500000208389752 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.060000000000000046 y2[1] (analytic) 0.059964006479444644 y2[1] (numeric) 0.06000000647944461 absolute error 3.5999999999966614e-05 relative error 0.06003601512568582% Correct digits 4 h 0.001 y1[1] (analytic) 0.9982005399352042 y1[1] (numeric) 0.9981999999352044 absolute error 5.399999998267901e-07 relative error 5.4097345996411e-05% Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.060075536247098466 Order of pole (six term test) -9.500000432168457 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.07000000000000005 y2[1] (analytic) 0.06994284733753281 y2[1] (numeric) 0.07000001400419936 absolute error 5.716666666655268e-05 relative error 0.08173339925764767% Correct digits 4 h 0.001 y1[1] (analytic) 0.9975510002532796 y1[1] (numeric) 0.9975499998366132 absolute error 1.0004166663968306e-06 relative error 0.00010028727013885239% Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.07011991226641343 Order of pole (six term test) -9.500000800758098 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.08000000000000006 y2[1] (analytic) 0.07991469396917275 y2[1] (numeric) 0.08000002730250572 absolute error 8.533333333296533e-05 relative error 0.1067805294554251% Correct digits 3 h 0.001 y1[1] (analytic) 0.9968017063026193 y1[1] (numeric) 0.9967999996359532 absolute error 1.7066666661014196e-06 relative error 0.00017121426009911867% Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.08017893139428124 Order of pole (six term test) -9.500001366279735 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.09000000000000007 y2[1] (analytic) 0.08987854919801111 y2[1] (numeric) 0.09000004919801004 absolute error 0.00012149999999892802 relative error 0.13518242237227462% Correct digits 3 h 0.001 y1[1] (analytic) 0.9959527330119943 y1[1] (numeric) 0.9959499992619947 absolute error 2.73374999959497e-06 relative error 0.00027448591775309155% Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.09025466612636719 Order of pole (six term test) -9.5000021889185 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.10000000000000007 y2[1] (analytic) 0.09983341664682822 y2[1] (numeric) 0.10000008331349212 absolute error 0.0001666666666639005 relative error 0.1669447688578087% Correct digits 3 h 0.001 y1[1] (analytic) 0.9950041652780257 y1[1] (numeric) 0.9949999986113595 absolute error 4.166666666249874e-06 relative error 0.00041875871595830125% Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.10034918087612534 Order of pole (six term test) -9.500003336943067 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.11000000000000008 y2[1] (analytic) 0.1097783008371749 y2[1] (numeric) 0.11000013417050172 absolute error 0.00022183333332682909 relative error 0.20207393595557302% Correct digits 3 h 0.001 y1[1] (analytic) 0.9939560979566968 y1[1] (numeric) 0.9939499975400304 absolute error 6.100416666376951e-06 relative error 0.0006137511182755202% Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.11046453139911525 Order of pole (six term test) -9.500004886727679 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.12000000000000009 y2[1] (analytic) 0.11971220728891946 y2[1] (numeric) 0.12000020728890523 absolute error 0.00028799999998577186 relative error 0.24057696913957838% Correct digits 3 h 0.001 y1[1] (analytic) 0.9928086358538663 y1[1] (numeric) 0.9927999958538667 absolute error 8.63999999956011e-06 relative error 0.0008702583446133372% Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.12060276373612212 Order of pole (six term test) -9.500006922776777 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.1300000000000001 y2[1] (analytic) 0.12963414261969494 y2[1] (numeric) 0.13000030928633238 absolute error 0.0003661666666374408 relative error 0.2824615947911628% Correct digits 3 h 0.001 y1[1] (analytic) 0.991561893714788 y1[1] (numeric) 0.991549993298122 absolute error 1.1900416665988622e-05 relative error 0.0012001688186508354% Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.13076591318358485 Order of pole (six term test) -9.500009537752176 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.1400000000000001 y2[1] (analytic) 0.13954311464423658 y2[1] (numeric) 0.14000044797751293 absolute error 0.00045733333327635517 relative error 0.3277362229174265% Correct digits 3 h 0.001 y1[1] (analytic) 0.9902159962126371 y1[1] (numeric) 0.9901999895459715 absolute error 1.6006666665568936e-05 relative error 0.0016164823358530854% Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.1409560036072045 Order of pole (six term test) -9.500012832502833 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.1500000000000001 y2[1] (analytic) 0.14943813247359933 y2[1] (numeric) 0.1500006324734933 absolute error 0.0005624999998939673 relative error 0.37640995011319617% Correct digits 3 h 0.001 y1[1] (analytic) 0.9887710779360422 y1[1] (numeric) 0.9887499841860441 absolute error 2.1093749998146727e-05 relative error 0.0021333299960773285% Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.15117504632745704 Order of pole (six term test) -9.50001691609714 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.16000000000000011 y2[1] (analytic) 0.1593182066142461 y2[1] (numeric) 0.1600008732807233 absolute error 0.0006826666664772052 relative error 0.4284925627678775% Correct digits 3 h 0.001 y1[1] (analytic) 0.9872272833756269 y1[1] (numeric) 0.9871999767089634 absolute error 2.7306666663506896e-05 relative error 0.002765995948788732% Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.161425039229438 Order of pole (six term test) -9.500021905857787 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.17000000000000012 y2[1] (analytic) 0.16918234906699614 y2[1] (numeric) 0.17000118240000262 absolute error 0.0008188333330064745 relative error 0.48399454051924584% Correct digits 3 h 0.001 y1[1] (analytic) 0.9855847669095607 y1[1] (numeric) 0.9855499664928997 absolute error 3.480041666092948e-05 relative error 0.0035309410036897253% Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.17170796593765214 Order of pole (six term test) -9.500027927399158 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.18000000000000013 y2[1] (analytic) 0.17902957342582432 y2[1] (numeric) 0.18000157342527767 absolute error 0.0009719999994533546 relative error 0.5429270599564235% Correct digits 3 h 0.001 y1[1] (analytic) 0.9838436927881213 y1[1] (numeric) 0.9837999527881314 absolute error 4.3739999989966805e-05 relative error 0.004445828164635759% Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.18202579490619475 Order of pole (six term test) -9.500035114667256 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.19000000000000014 y2[1] (analytic) 0.1888588949765007 y2[1] (numeric) 0.19000206164227812 absolute error 0.0011431666657774064 relative error 0.6053019985739343% Correct digits 3 h 0.001 y1[1] (analytic) 0.9820042351172703 y1[1] (numeric) 0.9819499347006205 absolute error 5.430041664977736e-05 relative error 0.0055295501493731174% Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.192380478464934 Order of pole (six term test) -9.500043609982136 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.20000000000000015 y2[1] (analytic) 0.19866933079506136 y2[1] (numeric) 0.20000266412698375 absolute error 0.0013333333319223983 relative error 0.6711319389794528% Correct digits 3 h 0.001 y1[1] (analytic) 0.9800665778412416 y1[1] (numeric) 0.9799999111746031 absolute error 6.666666663857068e-05 relative error 0.0068022589634078754% Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.20277395204785936 Order of pole (six term test) -9.500053564082865 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.21000000000000016 y2[1] (analytic) 0.20845989984609972 y2[1] (numeric) 0.21000339984391092 absolute error 0.0015434999978111985 relative error 0.7404301733574288% Correct digits 3 h 0.001 y1[1] (analytic) 0.9780309147241482 y1[1] (numeric) 0.9779498809741941 absolute error 8.103374995405144e-05 relative error 0.008285397601864851% Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.2132081333027123 Order of pole (six term test) -9.500065136174955 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.22000000000000017 y2[1] (analytic) 0.2182296230808695 y2[1] (numeric) 0.22000428974420927 absolute error 0.00177466666333978 relative error 0.8132107081915917% Correct digits 3 h 0.001 y1[1] (analytic) 0.9758974493306054 y1[1] (numeric) 0.9757998426640119 absolute error 9.760666659353046e-05 relative error 0.010001733958878725% Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.22368492124845388 Order of pole (six term test) -9.500078493980272 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.23000000000000018 y2[1] (analytic) 0.22797752353518858 y2[1] (numeric) 0.23000535686355847 absolute error 0.0020278333283698935 relative error 0.8894882692490057% Correct digits 3 h 0.001 y1[1] (analytic) 0.9736663950053748 y1[1] (numeric) 0.9735497945888221 absolute error 0.00011660041655270348 relative error 0.01197539703032062% Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.23420619545532803 Order of pole (six term test) -9.500093813789418 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.24000000000000019 y2[1] (analytic) 0.23770262642713477 y2[1] (numeric) 0.24000662641985473 absolute error 0.002303999992719963 relative error 0.9692783068285657% Correct digits 3 h 0.001 y1[1] (analytic) 0.9713379748520296 y1[1] (numeric) 0.971199734852204 absolute error 0.00013823999982554014 relative error 0.014231915502593128% Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.24477381524187497 Order of pole (six term test) -9.500111280516554 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.25000000000000017 y2[1] (analytic) 0.2474039592545231 y2[1] (numeric) 0.2500081259106776 absolute error 0.0026041666561545107 relative error 1.0525970012773354% Correct digits 3 h 0.001 y1[1] (analytic) 0.9689124217106447 y1[1] (numeric) 0.9687496612942409 absolute error 0.00016276041640383987 relative error 0.016798258826786566% Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.2553896188443311 Order of pole (six term test) -9.500131087756637 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2600000000000002 y2[1] (analytic) 0.2570805518921553 y2[1] (numeric) 0.2600098852105264 absolute error 0.002929333318371141 relative error 1.1394612687777292% Correct digits 3 h 0.001 y1[1] (analytic) 0.9663899781345132 y1[1] (numeric) 0.9661995714682354 absolute error 0.00019040666627778702 relative error 0.019702880885141386% Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.26605542265338655 Order of pole (six term test) -9.500153437845068 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2700000000000002 y2[1] (analytic) 0.2667314366888313 y2[1] (numeric) 0.2700119366678173 absolute error 0.0032804999789859957 relative error 1.229888767409529% Correct digits 3 h 0.001 y1[1] (analytic) 0.9637708963658904 y1[1] (numeric) 0.9635494626164578 absolute error 0.00022143374943262017 relative error 0.022975766363934075% Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.2767730204367737 Order of pole (six term test) -9.500178541919716 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2800000000000002 y2[1] (analytic) 0.27635564856411393 y2[1] (numeric) 0.28001431520162934 absolute error 0.0036586666375154064 relative error 1.3238979034896055% Correct digits 3 h 0.001 y1[1] (analytic) 0.9610554383107709 y1[1] (numeric) 0.9607993316449205 absolute error 0.00025610666585040853 relative error 0.02664847995663626% Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.28754418256850006 Order of pole (six term test) -9.500206619985308 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2900000000000002 y2[1] (analytic) 0.2859522251048357 y2[1] (numeric) 0.29001705839819136 absolute error 0.004064833293355663 relative error 1.4215078381940953% Correct digits 3 h 0.001 y1[1] (analytic) 0.9582438755126971 y1[1] (numeric) 0.9579491750971898 absolute error 0.0002947004155072763 relative error 0.03075421852809655% Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.29837065528451334 Order of pole (six term test) -9.500237900980132 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3000000000000002 y2[1] (analytic) 0.29552020666133977 y2[1] (numeric) 0.30002020660709877 absolute error 0.004499999945759003 relative error 1.5227384944664422% Correct digits 3 h 0.001 y1[1] (analytic) 0.955336489125606 y1[1] (numeric) 0.954998989127233 absolute error 0.00033749999837295874 relative error 0.035327866381599585% Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.3092541599496397 Order of pole (six term test) -9.500272622845054 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3100000000000002 y2[1] (analytic) 0.3050586364434437 y2[1] (numeric) 0.31002380303724997 absolute error 0.004965166593806247 relative error 1.6276105642158285% Correct digits 3 h 0.001 y1[1] (analytic) 0.9523335698857134 y1[1] (numeric) 0.951948769471305 absolute error 0.00038480041440835944 relative error 0.04040605377951112% Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.3201963923324952 Order of pole (six term test) -9.500311032594807 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.32000000000000023 y2[1] (analytic) 0.314566560616118 y2[1] (numeric) 0.3200278938524927 absolute error 0.00546133323637471 relative error 1.7361455158100738% Correct digits 3 h 0.001 y1[1] (analytic) 0.9492354180824408 y1[1] (numeric) 0.9487985114188765 absolute error 0.0004369066635643293 relative error 0.04602721887968829% Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.33119902189337214 Order of pole (six term test) -9.500353386391499 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.33000000000000024 y2[1] (analytic) 0.3240430283948686 y2[1] (numeric) 0.3300325282669711 absolute error 0.0059894998721025106 relative error 1.8483656018681245% Correct digits 3 h 0.001 y1[1] (analytic) 0.9460423435283869 y1[1] (numeric) 0.9455482097826071 absolute error 0.000494133745779779 relative error 0.05223167326071722% Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.34226369108353993 Order of pole (six term test) -9.500399949620341 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.34000000000000025 y2[1] (analytic) 0.3334870921408146 y2[1] (numeric) 0.3400377586401618 absolute error 0.0065506664993471575 relative error 1.9642938673563846% Correct digits 3 h 0.001 y1[1] (analytic) 0.9427546655283462 y1[1] (numeric) 0.942197858867368 absolute error 0.0005568066609782374 relative error 0.05906167122134445% Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.3533920146671143 Order of pole (six term test) -9.50045099696753 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.35000000000000026 y2[1] (analytic) 0.34289780745545156 y2[1] (numeric) 0.3500436405715904 absolute error 0.007145833116138811 relative error 2.083954157994195% Correct digits 3 h 0.001 y1[1] (analytic) 0.9393727128473789 y1[1] (numeric) 0.9387474524383135 absolute error 0.000625260409065409 relative error 0.06656148305289297% Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.3645855790322385 Order of pole (six term test) -9.500506812500252 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.36000000000000026 y2[1] (analytic) 0.3522742332750902 y2[1] (numeric) 0.3600502329952184 absolute error 0.007775999720128157 relative error 2.2073711289738003% Correct digits 3 h 0.001 y1[1] (analytic) 0.9358968236779348 y1[1] (numeric) 0.9351969836880097 absolute error 0.0006998399899250662 relative error 0.07477747249689336% Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.37584594153457646 Order of pole (six term test) -9.500567689748753 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3700000000000003 y2[1] (analytic) 0.3616154319649622 y2[1] (numeric) 0.37005759827348933 absolute error 0.008442166308527121 relative error 2.3345702539998636% Correct digits 3 h 0.001 y1[1] (analytic) 0.9323273456060344 y1[1] (numeric) 0.9315464452026183 absolute error 0.0007809004034160516 relative error 0.0837581786157359% Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.38717462983860623 Order of pole (six term test) -9.500633931790459 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3800000000000003 y2[1] (analytic) 0.37092046941298296 y2[1] (numeric) 0.3800658022910251 absolute error 0.009145332878042145 relative error 2.4655778346542876% Correct digits 3 h 0.001 y1[1] (analytic) 0.9286646355765101 y1[1] (numeric) 0.9277958289271439 absolute error 0.0008688066493662827 relative error 0.09355440231951248% Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.3985731412718097 Order of pole (six term test) -9.500705851336056 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3900000000000003 y2[1] (analytic) 0.3801884151231617 y2[1] (numeric) 0.39007491454796245 absolute error 0.009886499424800743 relative error 2.6004210100925933% Correct digits 3 h 0.001 y1[1] (analytic) 0.924909059857313 y1[1] (numeric) 0.9239451261297452 absolute error 0.0009639337275677562 relative error 0.10421929781036673% Correct digits 3 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.41004294218797777 Order of pole (six term test) -9.50078377081749 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4000000000000003 y2[1] (analytic) 0.38941834230865074 y2[1] (numeric) 0.40008500825291904 absolute error 0.010666665944268294 relative error 2.7391277670772776% Correct digits 3 h 0.001 y1[1] (analytic) 0.921060994002885 y1[1] (numeric) 0.9199943273651138 absolute error 0.0010666666377712186 relative error 0.11580846922368722% Correct digits 3 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.42158546733807706 Order of pole (six term test) -9.500868022477846 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4100000000000003 y2[1] (analytic) 0.39860932798442317 y2[1] (numeric) 0.4100961604155799 absolute error 0.011486832431156724 relative error 2.881726950355162% Correct digits 3 h 0.001 y1[1] (analytic) 0.917120822816605 y1[1] (numeric) 0.9159434224369272 absolute error 0.0011774003796778398 relative error 0.1283800727653179% Correct digits 3 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.4332021192497285 Order of pole (six term test) -9.500958948463012 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4200000000000003 y2[1] (analytic) 0.4077604530595705 y2[1] (numeric) 0.42010845193889346 absolute error 0.012347998879322974 relative error 3.028248273384921% Correct digits 3 h 0.001 y1[1] (analytic) 0.9130889403123081 y1[1] (numeric) 0.9117924003593763 absolute error 0.0012965399529318855 relative error 0.14199492466620214% Correct digits 3 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.4448942676108391 Order of pole (six term test) -9.501056900915076 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4300000000000003 y2[1] (analytic) 0.41687080242921104 y2[1] (numeric) 0.4301219677108675 absolute error 0.013251165281656485 relative error 3.1787223294216367% Correct digits 3 h 0.001 y1[1] (analytic) 0.908965749674885 y1[1] (numeric) 0.9075412493177734 absolute error 0.0014245003571116133 relative error 0.15671661529833467% Correct digits 3 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.4566632486632211 Order of pole (six term test) -9.5011622420674 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.44000000000000034 y2[1] (analytic) 0.4259394650659999 y2[1] (numeric) 0.44013679669595546 absolute error 0.014197331629955567 relative error 3.333180602965652% Correct digits 3 h 0.001 y1[1] (analytic) 0.9047516632199633 y1[1] (numeric) 0.9031899566282446 absolute error 0.0015617065917186146 relative error 0.1726116298212245% Correct digits 3 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.4685103645977104 Order of pole (six term test) -9.50127534434126 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.45000000000000034 y2[1] (analytic) 0.4349655341112305 y2[1] (numeric) 0.45015303202602186 absolute error 0.015187497914791348 relative error 3.491655481582953% Correct digits 3 h 0.001 y1[1] (analytic) 0.9004471023526768 y1[1] (numeric) 0.8987385086965106 absolute error 0.0017085936561661574 relative error 0.18974947575509607% Correct digits 3 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.4804368829548089 Order of pole (six term test) -9.501396590443996 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.46000000000000035 y2[1] (analytic) 0.44394810696552006 y2[1] (numeric) 0.4601707710908782 absolute error 0.01622266412535811 relative error 3.654180268104639% Correct digits 3 h 0.001 y1[1] (analytic) 0.8960524975255251 y1[1] (numeric) 0.894186890975758 absolute error 0.0018656065497670848 relative error 0.20820281790620654% Correct digits 3 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.492444036029552 Order of pole (six term test) -9.501526373468582 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.47000000000000036 y2[1] (analytic) 0.4528862853790686 y2[1] (numeric) 0.4701901156283787 absolute error 0.017303830249310093 relative error 3.82078919321363% Correct digits 3 h 0.001 y1[1] (analytic) 0.8915682881953287 y1[1] (numeric) 0.8895350879236107 absolute error 0.0020332002717180497 relative error 0.22804762110074145% Correct digits 3 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.5045330202770757 Order of pole (six term test) -9.501665096994511 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.48000000000000037 y2[1] (analytic) 0.46177917554148323 y2[1] (numeric) 0.4802111718140656 absolute error 0.01843199627258235 relative error 3.9915174284264667% Correct digits 3 h 0.001 y1[1] (analytic) 0.886994922779284 y1[1] (numeric) 0.8847830829581996 absolute error 0.002211839821084416 relative error 0.24936330121867006% Correct digits 3 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.5167049957213673 Order of pole (six term test) -9.501813175189904 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4900000000000004 y2[1] (analytic) 0.47062588817115836 y2[1] (numeric) 0.4902340503503541 absolute error 0.019608162179195754 relative error 4.166401099478958% Correct digits 3 h 0.001 y1[1] (analytic) 0.8823328586101213 y1[1] (numeric) 0.8799308584133403 absolute error 0.002402000196781051 relative error 0.2722328850548259% Correct digits 3 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.5289610853641995 Order of pole (six term test) -9.501971032914751 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * y2 ; Iterations 500 Total Elapsed Time 31.0 Seconds Elapsed Time(since restart) 31.0 Seconds Time to Timeout 2 Minutes 29.0 Seconds Percent Done 100.20000000000007%