##############ECHO OF PROBLEM################# ##############temp/sin_sqrt_linpostode.ode################# diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; ! #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=3.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=1000000 $glob_max_h=0.0001 #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(sin(sqrt(2.0*x+3.0))-sqrt(2.0*x+3.0)*cos(sqrt(2.0*x+3.0))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 10 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-10 range 1.0 estimated_steps 1000000.0 step_error 1.0e-16 est_needed_step_err 1.0e-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 9.919058284132172e-175 estimated_step_error 9.919058284132172e-175 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 6.656566452983411e-167 estimated_step_error 6.656566452983411e-167 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 4.467144945550478e-159 estimated_step_error 4.467144945550478e-159 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 2.997848639133688e-151 estimated_step_error 2.997848639133688e-151 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 2.011820036051395e-143 estimated_step_error 2.011820036051395e-143 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 1.3501067129414135e-135 estimated_step_error 1.3501067129414135e-135 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 9.060374406130706e-128 estimated_step_error 9.060374406130706e-128 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 6.0802628363317595e-120 estimated_step_error 6.0802628363317595e-120 best_h 0.0001 START of Soultion TOP MAIN SOLVE Loop x[1] 2.0 y[1] (analytic) 2.80289196959102 y[1] (numeric) 2.80289196959102 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 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 3.9946767760975557 Order of pole (six term test) -1.3631857114600834 TOP MAIN SOLVE Loop x[1] 2.010000000000021 y[1] (analytic) 2.8076330622967918 y[1] (numeric) 2.8076332285709915 absolute error 1.6627419974213353e-07 relative error 5.922219750686098e-06% Correct digits 8 h 0.0001 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 4.001927961798175 Order of pole (six term test) -1.3635188791105026 TOP MAIN SOLVE Loop x[1] 2.020000000000042 y[1] (analytic) 2.812340890281396 y[1] (numeric) 2.812341222929372 absolute error 3.326479758314349e-07 relative error 1.1828152731447536e-05% Correct digits 7 h 0.0001 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 4.00917198862828 Order of pole (six term test) -1.3638390346454106 TOP MAIN SOLVE Loop x[1] 2.0300000000000633 y[1] (analytic) 2.8170154339090487 y[1] (numeric) 2.817015933027591 absolute error 4.991185420522015e-07 relative error 1.7717991035625837e-05% Correct digits 7 h 0.0001 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 4.016408838818013 Order of pole (six term test) -1.3641461875425556 TOP MAIN SOLVE Loop x[1] 2.0400000000000844 y[1] (analytic) 2.8216566740992475 y[1] (numeric) 2.8216573397823774 absolute error 6.656831299522992e-07 relative error 2.3591925129048667e-05% Correct digits 7 h 0.0001 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 4.023638487620927 Order of pole (six term test) -1.3644403469005066 TOP MAIN SOLVE Loop x[1] 2.0500000000001055 y[1] (analytic) 2.8262645923231178 y[1] (numeric) 2.8262654246621115 absolute error 8.323389937281434e-07 relative error 2.9450144051940367e-05% Correct digits 7 h 0.0001 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 4.030860903179943 Order of pole (six term test) -1.3647215214033892 TOP MAIN SOLVE Loop x[1] 2.0600000000001266 y[1] (analytic) 2.83083917059979 y[1] (numeric) 2.83084016968319 absolute error 9.990834000106474e-07 relative error 3.529283508532788e-05% Correct digits 7 h 0.0001 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 4.038076046396266 Order of pole (six term test) -1.3649897194775722 TOP MAIN SOLVE Loop x[1] 2.0700000000001477 y[1] (analytic) 2.835380391492795 y[1] (numeric) 2.835381557406431 absolute error 1.1659136363029177e-06 relative error 4.112018407833729e-05% Correct digits 7 h 0.0001 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 4.045283870255542 Order of pole (six term test) -1.3652449507167592 TOP MAIN SOLVE Loop x[1] 2.080000000000169 y[1] (analytic) 2.8398882381064965 y[1] (numeric) 2.8398895709335035 absolute error 1.3328270069834502e-06 relative error 4.6932375334323596e-05% Correct digits 7 h 0.0001 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 4.052484321042233 Order of pole (six term test) -1.3654872224464292 TOP MAIN SOLVE Loop x[1] 2.09000000000019 y[1] (analytic) 2.8443626940825504 y[1] (numeric) 2.844364193903386 absolute error 1.4998208355265774e-06 relative error 5.272959171651437e-05% Correct digits 7 h 0.0001 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 4.059677336644653 Order of pole (six term test) -1.365716543916406 TOP MAIN SOLVE Loop x[1] 2.100000000000211 y[1] (analytic) 2.848803743596383 y[1] (numeric) 2.848805410488842 absolute error 1.666892459173397e-06 relative error 5.8512014487494346e-05% Correct digits 7 h 0.0001 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 4.066862847916829 Order of pole (six term test) -1.3659329224780148 TOP MAIN SOLVE Loop x[1] 2.110000000000232 y[1] (analytic) 2.853211371353707 y[1] (numeric) 2.853213205392947 absolute error 1.8340392400340022e-06 relative error 6.427982372591772e-05% Correct digits 7 h 0.0001 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 4.074040777798363 Order of pole (six term test) -1.3661363656505632 TOP MAIN SOLVE Loop x[1] 2.1200000000002532 y[1] (analytic) 2.857585562587055 y[1] (numeric) 2.8575875638456028 absolute error 2.0012585477680034e-06 relative error 7.003319774460948e-05% Correct digits 7 h 0.0001 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 4.081211040986917 Order of pole (six term test) -1.3663268818207772 TOP MAIN SOLVE Loop x[1] 2.1300000000002743 y[1] (analytic) 2.861926303052344 y[1] (numeric) 2.8619284716001214 absolute error 2.1685477773480955e-06 relative error 7.577231373970965e-05% Correct digits 7 h 0.0001 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 4.088373545018978 Order of pole (six term test) -1.3665044771839536 TOP MAIN SOLVE Loop x[1] 2.1400000000002954 y[1] (analytic) 2.8662335790254656 y[1] (numeric) 2.866235914929801 absolute error 2.335904335293293e-06 relative error 8.149734733369193e-05% Correct digits 7 h 0.0001 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 4.0955281886195625 Order of pole (six term test) -1.366669159907003 TOP MAIN SOLVE Loop x[1] 2.1500000000003165 y[1] (analytic) 2.8705073772988987 y[1] (numeric) 2.870509880624546 absolute error 2.503325647218446e-06 relative error 8.720847286496213e-05% Correct digits 7 h 0.0001 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 4.102674863798787 Order of pole (six term test) -1.366820934501451 TOP MAIN SOLVE Loop x[1] 2.1600000000003376 y[1] (analytic) 2.874747685178352 y[1] (numeric) 2.8747503559875067 absolute error 2.6708091547256174e-06 relative error 9.29058633039622e-05% Correct digits 7 h 0.0001 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 4.109813453023675 Order of pole (six term test) -1.3669598091592512 TOP MAIN SOLVE Loop x[1] 2.1700000000003588 y[1] (analytic) 2.878954490479429 y[1] (numeric) 2.878957328831745 absolute error 2.8383523162922586e-06 relative error 9.858969030870617e-05% Correct digits 7 h 0.0001 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 4.116943832497281 Order of pole (six term test) -1.3670857870620647 TOP MAIN SOLVE Loop x[1] 2.18000000000038 y[1] (analytic) 2.8831277815243164 y[1] (numeric) 2.8831307874769276 absolute error 3.0059526112680146e-06 relative error 0.0001042601243875067% Correct digits 6 h 0.0001 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 4.124065868688702 Order of pole (six term test) -1.3671988754362765 TOP MAIN SOLVE Loop x[1] 2.190000000000401 y[1] (analytic) 2.887267547138503 y[1] (numeric) 2.8872707207460304 absolute error 3.1736075274402253e-06 relative error 0.00010991733449106601% Correct digits 6 h 0.0001 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 4.131179421659107 Order of pole (six term test) -1.367299076892749 TOP MAIN SOLVE Loop x[1] 2.200000000000422 y[1] (analytic) 2.891373776647514 y[1] (numeric) 2.8913771179620866 absolute error 3.341314572580245e-06 relative error 0.00011556148843732089% Correct digits 6 h 0.0001 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 4.138284342658522 Order of pole (six term test) -1.3673863957499695 TOP MAIN SOLVE Loop x[1] 2.210000000000443 y[1] (analytic) 2.8954464598736793 y[1] (numeric) 2.895449968944953 absolute error 3.5090712735552643e-06 relative error 0.00012119275290306546% Correct digits 6 h 0.0001 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 4.145380474773862 Order of pole (six term test) -1.3674608364901797 TOP MAIN SOLVE Loop x[1] 2.2200000000004643 y[1] (analytic) 2.899485587132917 y[1] (numeric) 2.8994892640080807 absolute error 3.6768751638938113e-06 relative error 0.00012681129301731059% Correct digits 6 h 0.0001 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 4.152467654174642 Order of pole (six term test) -1.367522400624292 TOP MAIN SOLVE Loop x[1] 2.2300000000004854 y[1] (analytic) 2.9034911492315456 y[1] (numeric) 2.903494993955354 absolute error 3.844723808210659e-06 relative error 0.00013241727322737753% Correct digits 6 h 0.0001 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 4.159545709224731 Order of pole (six term test) -1.3675710893101751 TOP MAIN SOLVE Loop x[1] 2.2400000000005065 y[1] (analytic) 2.907463137463121 y[1] (numeric) 2.9074671500778932 absolute error 4.012614772452849e-06 relative error 0.00013801085629426132% Correct digits 6 h 0.0001 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 4.1666144603522195 Order of pole (six term test) -1.3676069040164887 TOP MAIN SOLVE Loop x[1] 2.2500000000005276 y[1] (analytic) 2.911401543605288 y[1] (numeric) 2.911405724150934 absolute error 4.18054564610415e-06 relative error 0.00014359220408076165% Correct digits 6 h 0.0001 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 4.1736737202964465 Order of pole (six term test) -1.367629846298307 TOP MAIN SOLVE Loop x[1] 2.2600000000005487 y[1] (analytic) 2.9153063599166655 y[1] (numeric) 2.9153107084306993 absolute error 4.348514033747364e-06 relative error 0.0001491614772819851% Correct digits 6 h 0.0001 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 4.180723296045986 Order of pole (six term test) -1.367639913153937 TOP MAIN SOLVE Loop x[1] 2.27000000000057 y[1] (analytic) 2.919177579133748 y[1] (numeric) 2.919182095651297 absolute error 4.5165175488470766e-06 relative error 0.00015471883523397476% Correct digits 6 h 0.0001 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 4.187762986055259 Order of pole (six term test) -1.3676371050579963 TOP MAIN SOLVE Loop x[1] 2.280000000000591 y[1] (analytic) 2.9230151944678293 y[1] (numeric) 2.9230198790216577 absolute error 4.684553828404603e-06 relative error 0.00016026443643778196% Correct digits 6 h 0.0001 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 4.194792583562757 Order of pole (six term test) -1.3676214178475394 TOP MAIN SOLVE Loop x[1] 2.290000000000612 y[1] (analytic) 2.9268191996019532 y[1] (numeric) 2.9268240522224747 absolute error 4.852620521411666e-06 relative error 0.0001657984381840744% Correct digits 6 h 0.0001 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 4.201811874520673 Order of pole (six term test) -1.3675928491563951 TOP MAIN SOLVE Loop x[1] 2.300000000000633 y[1] (analytic) 2.93058958868788 y[1] (numeric) 2.9305946094031707 absolute error 5.020715290626754e-06 relative error 0.00017132099663517506% Correct digits 6 h 0.0001 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 4.208820639760959 Order of pole (six term test) -1.3675513936306292 TOP MAIN SOLVE Loop x[1] 2.310000000000654 y[1] (analytic) 2.9343263563430804 y[1] (numeric) 2.9343315451788974 absolute error 5.188835817016013e-06 relative error 0.0001768322669971389% Correct digits 6 h 0.0001 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 4.215818654246316 Order of pole (six term test) -1.367497046126406 TOP MAIN SOLVE Loop x[1] 2.3200000000006753 y[1] (analytic) 2.938029497647745 y[1] (numeric) 2.9380348546275354 absolute error 5.356979790427374e-06 relative error 0.00018233240322182935% Correct digits 6 h 0.0001 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 4.222805688816739 Order of pole (six term test) -1.3674297984103951 TOP MAIN SOLVE Loop x[1] 2.3300000000006964 y[1] (analytic) 2.941699008141823 y[1] (numeric) 2.9417045332867464 absolute error 5.525144923357317e-06 relative error 0.000187821558496135% Correct digits 6 h 0.0001 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 4.229781509210448 Order of pole (six term test) -1.367349643396718 TOP MAIN SOLVE Loop x[1] 2.3400000000007175 y[1] (analytic) 2.945334883822073 y[1] (numeric) 2.94534057715101 absolute error 5.693328936740016e-06 relative error 0.00019329988477751478% Correct digits 6 h 0.0001 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 4.236745878360979 Order of pole (six term test) -1.3672565707385207 TOP MAIN SOLVE Loop x[1] 2.3500000000007386 y[1] (analytic) 2.9489371211391426 y[1] (numeric) 2.9489429826687124 absolute error 5.861529569717305e-06 relative error 0.0001987675331460801% Correct digits 6 h 0.0001 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 4.243698556441313 Order of pole (six term test) -1.367150568795127 TOP MAIN SOLVE Loop x[1] 2.3600000000007597 y[1] (analytic) 2.952505716994662 y[1] (numeric) 2.952511746739233 absolute error 6.029744571200979e-06 relative error 0.00020422465353728833% Correct digits 6 h 0.0001 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 4.250639300847344 Order of pole (six term test) -1.3670316270978216 TOP MAIN SOLVE Loop x[1] 2.370000000000781 y[1] (analytic) 2.956040668738365 y[1] (numeric) 2.9560468667100768 absolute error 6.197971711863204e-06 relative error 0.00020967139516752628% Correct digits 6 h 0.0001 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 4.257567869290946 Order of pole (six term test) -1.366899730533774 TOP MAIN SOLVE Loop x[1] 2.380000000000802 y[1] (analytic) 2.9595419741652242 y[1] (numeric) 2.9595483403739964 absolute error 6.366208772146109e-06 relative error 0.00021510790614624677% Correct digits 6 h 0.0001 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 4.264484019463202 Order of pole (six term test) -1.3667548633400788 TOP MAIN SOLVE Loop x[1] 2.390000000000823 y[1] (analytic) 2.963009631512609 y[1] (numeric) 2.963016165966155 absolute error 6.5344535462585895e-06 relative error 0.00022053433363032195% Correct digits 6 h 0.0001 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 4.2713875103696815 Order of pole (six term test) -1.3665970089118975 TOP MAIN SOLVE Loop x[1] 2.400000000000844 y[1] (analytic) 2.9664436394574647 y[1] (numeric) 2.9664503421613055 absolute error 6.702703840844038e-06 relative error 0.00022595082379754569% Correct digits 6 h 0.0001 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 4.2782781046018865 Order of pole (six term test) -1.3664261473757264 TOP MAIN SOLVE Loop x[1] 2.4100000000008652 y[1] (analytic) 2.969843997113508 y[1] (numeric) 2.969850868070992 absolute error 6.870957483862128e-06 relative error 0.00023135752216413535% Correct digits 6 h 0.0001 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 4.285155568464115 Order of pole (six term test) -1.3662422597454942 TOP MAIN SOLVE Loop x[1] 2.4200000000008863 y[1] (analytic) 2.973210704028445 y[1] (numeric) 2.973217743240754 absolute error 7.039212309045695e-06 relative error 0.00023675457307846255% Correct digits 6 h 0.0001 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 4.2920196757288815 Order of pole (six term test) -1.3660453222779338 TOP MAIN SOLVE Loop x[1] 2.4300000000009074 y[1] (analytic) 2.9765437601812073 y[1] (numeric) 2.9765509676473743 absolute error 7.207466167002963e-06 relative error 0.0002421421201133016% Correct digits 6 h 0.0001 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 4.298870208234145 Order of pole (six term test) -1.3658353104601257 TOP MAIN SOLVE Loop x[1] 2.4400000000009285 y[1] (analytic) 2.979843165979207 y[1] (numeric) 2.9798505416961323 absolute error 7.375716925217546e-06 relative error 0.0002475203060827468% Correct digits 6 h 0.0001 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 4.30570695837009 Order of pole (six term test) -1.3656121983084866 TOP MAIN SOLVE Loop x[1] 2.4500000000009496 y[1] (analytic) 2.983108922255612 y[1] (numeric) 2.983116466218068 absolute error 7.54396245605804e-06 relative error 0.00025288927265699167% Correct digits 6 h 0.0001 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 4.312529731917069 Order of pole (six term test) -1.3653759573661741 TOP MAIN SOLVE Loop x[1] 2.4600000000009707 y[1] (analytic) 2.9863410302666367 y[1] (numeric) 2.9863487424672943 absolute error 7.712200657650214e-06 relative error 0.0002582491610799597% Correct digits 6 h 0.0001 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 4.3193383510235055 Order of pole (six term test) -1.3651265561245278 TOP MAIN SOLVE Loop x[1] 2.470000000000992 y[1] (analytic) 2.9895394916888582 y[1] (numeric) 2.989547372118287 absolute error 7.880429428563929e-06 relative error 0.00026360011133728483% Correct digits 6 h 0.0001 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 4.326132656226877 Order of pole (six term test) -1.3648639633083715 TOP MAIN SOLVE Loop x[1] 2.480000000001013 y[1] (analytic) 2.992704308616539 y[1] (numeric) 2.9927123572632306 absolute error 8.048646691793948e-06 relative error 0.0002689422629766808% Correct digits 6 h 0.0001 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 4.332912512024876 Order of pole (six term test) -1.364588141550156 TOP MAIN SOLVE Loop x[1] 2.490000000001034 y[1] (analytic) 2.9958354835589844 y[1] (numeric) 2.9958437004093645 absolute error 8.216850380105e-06 relative error 0.00027427575463334755% Correct digits 6 h 0.0001 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 4.339677808192109 Order of pole (six term test) -1.364299055164155 TOP MAIN SOLVE Loop x[1] 2.500000000001055 y[1] (analytic) 2.9989330194379025 y[1] (numeric) 2.9989414044763336 absolute error 8.385038431146796e-06 relative error 0.00027960072388407076% Correct digits 6 h 0.0001 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 4.346428466332274 Order of pole (six term test) -1.3639966633510152 TOP MAIN SOLVE Loop x[1] 2.5100000000010763 y[1] (analytic) 3.0019969195847884 y[1] (numeric) 3.002005472793596 absolute error 8.55320880743804e-06 relative error 0.00028491730793051744% Correct digits 6 h 0.0001 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 4.353164443322935 Order of pole (six term test) -1.3636809244244787 TOP MAIN SOLVE Loop x[1] 2.5200000000010974 y[1] (analytic) 3.005027187738331 y[1] (numeric) 3.005035909097807 absolute error 8.721359475938328e-06 relative error 0.00029022564293344283% Correct digits 6 h 0.0001 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 4.359885737626459 Order of pole (six term test) -1.3633517928793157 TOP MAIN SOLVE Loop x[1] 2.5300000000011185 y[1] (analytic) 3.008023828041829 y[1] (numeric) 3.0080327175302535 absolute error 8.889488424479453e-06 relative error 0.00029552586457622424% Correct digits 6 h 0.0001 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 4.366592394576183 Order of pole (six term test) -1.3630092215900547 TOP MAIN SOLVE Loop x[1] 2.5400000000011396 y[1] (analytic) 3.010986845040628 y[1] (numeric) 3.010995902634276 absolute error 9.05759364799863e-06 relative error 0.0003008181076220017% Correct digits 6 h 0.0001 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 4.373284513537725 Order of pole (six term test) -1.362653160241333 TOP MAIN SOLVE Loop x[1] 2.5500000000011607 y[1] (analytic) 3.013916243679576 y[1] (numeric) 3.0139254693527286 absolute error 9.225673152535308e-06 relative error 0.0003061025060627442% Correct digits 6 h 0.0001 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 4.379962254951029 Order of pole (six term test) -1.3622835565770526 TOP MAIN SOLVE Loop x[1] 2.5600000000011818 y[1] (analytic) 3.0168120293004947 y[1] (numeric) 3.016821423025455 absolute error 9.393724960116145e-06 relative error 0.00031137919329678155% Correct digits 6 h 0.0001 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 4.386625848939608 Order of pole (six term test) -1.361900355310457 TOP MAIN SOLVE Loop x[1] 2.570000000001203 y[1] (analytic) 3.0196742076396657 y[1] (numeric) 3.0196837693867753 absolute error 9.561747109643193e-06 relative error 0.0003166483021728742% Correct digits 6 h 0.0001 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 4.393275604611298 Order of pole (six term test) -1.3615034978114107 TOP MAIN SOLVE Loop x[1] 2.580000000001224 y[1] (analytic) 3.0225027848253374 y[1] (numeric) 3.0225125145629805 absolute error 9.729737643127123e-06 relative error 0.00032190996454911056% Correct digits 6 h 0.0001 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 4.3999119198802275 Order of pole (six term test) -1.3610929235989122 TOP MAIN SOLVE Loop x[1] 2.590000000001245 y[1] (analytic) 3.0252977673752475 y[1] (numeric) 3.0253076650698647 absolute error 9.897694617233554e-06 relative error 0.0003271643116909053% Correct digits 6 h 0.0001 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 4.40653529320287 Order of pole (six term test) -1.3606685693439609 TOP MAIN SOLVE Loop x[1] 2.600000000001266 y[1] (analytic) 3.0280591621941597 y[1] (numeric) 3.0280692278102657 absolute error 1.0065616105947583e-05 relative error 0.00033241147437337203% Correct digits 6 h 0.0001 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 4.413146336146982 Order of pole (six term test) -1.3602303694709406 TOP MAIN SOLVE Loop x[1] 2.6100000000012873 y[1] (analytic) 3.030786976571416 y[1] (numeric) 3.030797210071608 absolute error 1.0233500191692002e-05 relative error 0.00033765158260210914% Correct digits 6 h 0.0001 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 4.419745788078418 Order of pole (six term test) -1.3597782544238726 TOP MAIN SOLVE Loop x[1] 2.6200000000013084 y[1] (analytic) 3.033481218178512 y[1] (numeric) 3.0334916195234856 absolute error 1.0401344973764992e-05 relative error 0.0003428847659063667% Correct digits 6 h 0.0001 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 4.426334530860896 Order of pole (six term test) -1.3593121546578502 TOP MAIN SOLVE Loop x[1] 2.6300000000013295 y[1] (analytic) 3.0361418950666788 y[1] (numeric) 3.0361524642152316 absolute error 1.0569148552797003e-05 relative error 0.00034811115284073005% Correct digits 6 h 0.0001 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 4.432913607954664 Order of pole (six term test) -1.358831995421017 TOP MAIN SOLVE Loop x[1] 2.6400000000013506 y[1] (analytic) 3.03876901566449 y[1] (numeric) 3.0387797525735385 absolute error 1.073690904851432e-05 relative error 0.00035333087158539664% Correct digits 6 h 0.0001 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 4.439484242725741 Order of pole (six term test) -1.3583377016128253 TOP MAIN SOLVE Loop x[1] 2.6500000000013717 y[1] (analytic) 3.041362588775474 y[1] (numeric) 3.0413734934000685 absolute error 1.0904624594409995e-05 relative error 0.0003585440497839641% Correct digits 6 h 0.0001 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 4.446047860763065 Order of pole (six term test) -1.3578291964268985 TOP MAIN SOLVE Loop x[1] 2.660000000001393 y[1] (analytic) 3.043922623575755 y[1] (numeric) 3.0439336958690912 absolute error 1.1072293336411576e-05 relative error 0.00036375081451330514% Correct digits 6 h 0.0001 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 4.452606114798878 Order of pole (six term test) -1.3573063995982135 TOP MAIN SOLVE Loop x[1] 2.670000000001414 y[1] (analytic) 3.046449129611695 y[1] (numeric) 3.046460369525121 absolute error 1.1239913425775683e-05 relative error 0.000368951292064028% Correct digits 6 h 0.0001 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 4.459160910714897 Order of pole (six term test) -1.3567692321987934 TOP MAIN SOLVE Loop x[1] 2.680000000001435 y[1] (analytic) 3.0489421167975626 y[1] (numeric) 3.048953524280591 absolute error 1.1407483028413878e-05 relative error 0.0003741456082608632% Correct digits 6 h 0.0001 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 4.465714439369416 Order of pole (six term test) -1.3562176114428688 TOP MAIN SOLVE Loop x[1] 2.690000000001456 y[1] (analytic) 3.0514015954132114 y[1] (numeric) 3.0514131704135354 absolute error 1.1575000324004492e-05 relative error 0.00037933388844666447% Correct digits 6 h 0.0001 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 4.472269209298736 Order of pole (six term test) -1.355651455505777 TOP MAIN SOLVE Loop x[1] 2.700000000001477 y[1] (analytic) 3.0538275761017757 y[1] (numeric) 3.0538393185652772 absolute error 1.1742463501551725e-05 relative error 0.00038451625735009675% Correct digits 6 h 0.0001 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 4.478828084823259 Order of pole (six term test) -1.355070682951725 TOP MAIN SOLVE Loop x[1] 2.7100000000014983 y[1] (analytic) 3.056220069867378 y[1] (numeric) 3.056231979738137 absolute error 1.1909870759385655e-05 relative error 0.00038969283909919727% Correct digits 6 h 0.0001 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 4.485394328270552 Order of pole (six term test) -1.3544752132269018 TOP MAIN SOLVE Loop x[1] 2.7200000000015194 y[1] (analytic) 3.0585790880728543 y[1] (numeric) 3.058591165293167 absolute error 1.2077220312711745e-05 relative error 0.0003948637574816267% Correct digits 6 h 0.0001 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 4.491971647971683 Order of pole (six term test) -1.3538649639656626 TOP MAIN SOLVE Loop x[1] 2.7300000000015405 y[1] (analytic) 3.0609046424374933 y[1] (numeric) 3.0609168869478776 absolute error 1.2244510384284979e-05 relative error 0.0004000291356523376% Correct digits 6 h 0.0001 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 4.498564248633415 Order of pole (six term test) -1.3532398606899143 TOP MAIN SOLVE Loop x[1] 2.7400000000015616 y[1] (analytic) 3.0631967450347917 y[1] (numeric) 3.0632091567739987 absolute error 1.241173920707439e-05 relative error 0.0004051890962339547% Correct digits 6 h 0.0001 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 4.505176892308953 Order of pole (six term test) -1.352599829242509 TOP MAIN SOLVE Loop x[1] 2.7500000000015827 y[1] (analytic) 3.065455408290216 y[1] (numeric) 3.065467987195242 absolute error 1.2578905026039422e-05 relative error 0.0004103437613876567% Correct digits 6 h 0.0001 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 4.511814963211421 Order of pole (six term test) -1.3519448003033698 TOP MAIN SOLVE Loop x[1] 2.760000000001604 y[1] (analytic) 3.067680644978992 y[1] (numeric) 3.0676933909850925 absolute error 1.2746006100350371e-05 relative error 0.0004154932528981568% Correct digits 6 h 0.0001 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 4.518484540480042 Order of pole (six term test) -1.3512747130865534 TOP MAIN SOLVE Loop x[1] 2.770000000001625 y[1] (analytic) 3.069872468223898 y[1] (numeric) 3.069885381264595 absolute error 1.2913040697171141e-05 relative error 0.00042063769198340983% Correct digits 6 h 0.0001 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 4.525192481420423 Order of pole (six term test) -1.3505895119737925 TOP MAIN SOLVE Loop x[1] 2.780000000001646 y[1] (analytic) 3.0720308914930703 y[1] (numeric) 3.072043971500165 absolute error 1.3080007094767865e-05 relative error 0.0004257771994086528% Correct digits 6 h 0.0001 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 4.531946511286068 Order of pole (six term test) -1.3498891552658723 TOP MAIN SOLVE Loop x[1] 2.790000000001667 y[1] (analytic) 3.0741559285978366 y[1] (numeric) 3.074169175501418 absolute error 1.3246903581620728e-05 relative error 0.0004309118954698832% Correct digits 6 h 0.0001 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 4.538755327336279 Order of pole (six term test) -1.349173610440241 TOP MAIN SOLVE Loop x[1] 2.8000000000016882 y[1] (analytic) 3.0762475936905456 y[1] (numeric) 3.076261007419004 absolute error 1.3413728458644414e-05 relative error 0.00043604190007840327% Correct digits 6 h 0.0001 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 4.545628711149343 Order of pole (six term test) -1.3484428639411945 TOP MAIN SOLVE Loop x[1] 2.8100000000017094 y[1] (analytic) 3.078305901262423 y[1] (numeric) 3.0783194817424597 absolute error 1.3580480036523568e-05 relative error 0.00044116733268627297% Correct digits 6 h 0.0001 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 4.55257765759785 Order of pole (six term test) -1.347696918533753 TOP MAIN SOLVE Loop x[1] 2.8200000000017305 y[1] (analytic) 3.080330866141435 y[1] (numeric) 3.0803446132980765 absolute error 1.3747156641485958e-05 relative error 0.00044628831248593376% Correct digits 6 h 0.0001 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 4.559614515527802 Order of pole (six term test) -1.3469358025687974 TOP MAIN SOLVE Loop x[1] 2.8300000000017516 y[1] (analytic) 3.082322503490167 y[1] (numeric) 3.0823364172467635 absolute error 1.3913756596650728e-05 relative error 0.0004514049578165796% Correct digits 6 h 0.0001 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 4.5667531480661845 Order of pole (six term test) -1.3461595679391678 TOP MAIN SOLVE Loop x[1] 2.8400000000017727 y[1] (analytic) 3.0842808288037156 y[1] (numeric) 3.084294909081966 absolute error 1.4080278250450107e-05 relative error 0.0004565173870990001% Correct digits 6 h 0.0001 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 4.5740091071970905 Order of pole (six term test) -1.3453683025703675 TOP MAIN SOLVE Loop x[1] 2.8500000000017938 y[1] (analytic) 3.086205857907592 y[1] (numeric) 3.08622010462755 absolute error 1.424671995797766e-05 relative error 0.0004616257182415159% Correct digits 6 h 0.0001 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 4.581399832211586 Order of pole (six term test) -1.3445621300481463 TOP MAIN SOLVE Loop x[1] 2.860000000001815 y[1] (analytic) 3.0880976069556434 y[1] (numeric) 3.088112020035721 absolute error 1.441308007743558e-05 relative error 0.0004667300685370664% Correct digits 6 h 0.0001 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 4.588944867069013 Order of pole (six term test) -1.3437412204641692 TOP MAIN SOLVE Loop x[1] 2.870000000001836 y[1] (analytic) 3.0899560924279776 y[1] (numeric) 3.089970671784963 absolute error 1.4579356985233716e-05 relative error 0.0004718305551642248% Correct digits 6 h 0.0001 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 4.596666103819979 Order of pole (six term test) -1.3429057962845192 TOP MAIN SOLVE Loop x[1] 2.880000000001857 y[1] (analytic) 3.091781331128915 y[1] (numeric) 3.0917960766779804 absolute error 1.4745549065331431e-05 relative error 0.0004769272948532659% Correct digits 6 h 0.0001 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 4.60458805068295 Order of pole (six term test) -1.342056143563065 TOP MAIN SOLVE Loop x[1] 2.890000000001878 y[1] (analytic) 3.093573340184939 y[1] (numeric) 3.0935882518396522 absolute error 1.4911654713234412e-05 relative error 0.0004820204040271102% Correct digits 6 h 0.0001 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 4.612738130969632 Order of pole (six term test) -1.3411926182189475 TOP MAIN SOLVE Loop x[1] 2.9000000000018993 y[1] (analytic) 3.0953321370426665 y[1] (numeric) 3.095347214714997 absolute error 1.5077672330665592e-05 relative error 0.00048710999864043863% Correct digits 6 h 0.0001 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 4.621147008922022 Order of pole (six term test) -1.340315663410749 TOP MAIN SOLVE Loop x[1] 2.9100000000019204 y[1] (analytic) 3.0970577394668313 y[1] (numeric) 3.0970729830671653 absolute error 1.524360033400285e-05 relative error 0.0004921961944638167% Correct digits 6 h 0.0001 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 4.6298489508443685 Order of pole (six term test) -1.3394258207396366 TOP MAIN SOLVE Loop x[1] 2.9200000000019415 y[1] (analytic) 3.0987501655382754 y[1] (numeric) 3.0987655749754226 absolute error 1.5409437147173577e-05 relative error 0.0004972791068652302% Correct digits 6 h 0.0001 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 4.638882220353191 Order of pole (six term test) -1.3385237443224316 TOP MAIN SOLVE Loop x[1] 2.9300000000019626 y[1] (analytic) 3.100409433651958 y[1] (numeric) 3.1004250088331644 absolute error 1.5575181206539668e-05 relative error 0.0005023588509790377% Correct digits 6 h 0.0001 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 4.648289506120786 Order of pole (six term test) -1.3376102227944848 TOP MAIN SOLVE Loop x[1] 2.9400000000019837 y[1] (analytic) 3.102035562514973 y[1] (numeric) 3.102051303345926 absolute error 1.5740830952903906e-05 relative error 0.0005074355414591713% 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 6.73704366366962 Order of pole (three term test) 4.287340860055223 Radius of convergence (six term test) for eq 1 4.658118387828405 Order of pole (six term test) -1.3366861977747 TOP MAIN SOLVE Loop x[1] 2.950000000002005 y[1] (analytic) 3.1036285711445792 y[1] (numeric) 3.103644477529419 absolute error 1.5906384839947663e-05 relative error 0.0005125092927624902% 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 6.399177786908455 Order of pole (three term test) 3.0865123480320715 Radius of convergence (six term test) for eq 1 4.66842183640993 Order of pole (six term test) -1.3357527869587056 TOP MAIN SOLVE Loop x[1] 2.960000000002026 y[1] (analytic) 3.1051884788662436 y[1] (numeric) 3.1052045507075796 absolute error 1.6071841336007253e-05 relative error 0.0005175802192166883% 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 6.1350627408525344 Order of pole (three term test) 2.150088248318934 Radius of convergence (six term test) for eq 1 4.679258745817704 Order of pole (six term test) -1.3348113118031542 TOP MAIN SOLVE Loop x[1] 2.970000000002047 y[1] (analytic) 3.1067153053116967 y[1] (numeric) 3.1067315425106052 absolute error 1.6237198908530814e-05 relative error 0.0005226484345304932% 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 5.9241972872002515 Order of pole (three term test) 1.4039535633119258 Radius of convergence (six term test) for eq 1 4.6906944929034715 Order of pole (six term test) -1.3338633286047212 TOP MAIN SOLVE Loop x[1] 2.980000000002068 y[1] (analytic) 3.1082090704169967 y[1] (numeric) 3.108225472873042 absolute error 1.6402456045394587e-05 relative error 0.0005277140524911356% 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 5.752980175609299 Order of pole (three term test) 0.7989907832427674 Radius of convergence (six term test) for eq 1 4.702801520370899 Order of pole (six term test) -1.3329106599887073 TOP MAIN SOLVE Loop x[1] 2.990000000002089 y[1] (analytic) 3.1096697944206104 y[1] (numeric) 3.1096863620318502 absolute error 1.656761123980388e-05 relative error 0.0005327771864887261% 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 5.612037870050423 Order of pole (three term test) 0.3013930318493565 Radius of convergence (six term test) for eq 1 4.715659926580376 Order of pole (six term test) -1.3319554356009533 Finished! diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations 10000 Total Elapsed Time 14 Seconds Elapsed Time(since restart) 14 Seconds Time to Timeout 29 Minutes 46.0 Seconds Percent Done 100.01000000021105%