##############ECHO OF PROBLEM################# ##############temp/sp_mtest6_3postode.ode################# diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ t_start=1.5; t_end=1.6; array_x1_init[0 + 1] = exact_soln_x1(t_start); array_x1_init[1 + 1] = exact_soln_x1p(t_start); array_x2_init[0 + 1] = exact_soln_x2(t_start); array_x2_init[1 + 1] = exact_soln_x2p(t_start); glob_max_iter=1000000000; glob_display_interval=0.001; glob_max_minutes=2; glob_desired_digits_correct=10; glob_look_poles=true; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_x1 (double t) { double c1,c2,c3; c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return(2.0 * c1 + 6.0 * c3 * exp(-t)); } double exact_soln_x1p (double t) { double c1,c2,c3; c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return( - 6.0 * c3 * exp(-t)); } double exact_soln_x2 (double t) { double c1,c2,c3; c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t)); } double exact_soln_x2p (double t) { double c1,c2,c3; c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 0.1000000000000001 estimated_steps = 100.0000000000001 step_error = 9.999999999999992e-13 est_needed_step_err = 9.999999999999992e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 1.193323441522736e+50 max_value3 = 1.193323441522736e+50 value3 = 1.193323441522736e+50 best_h = 0 opt_iter = 2 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 0.1000000000000001 estimated_steps = 200.0000000000002 step_error = 4.999999999999996e-13 est_needed_step_err = 4.999999999999996e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 4.445774813306187e+41 max_value3 = 4.445774813306187e+41 value3 = 4.445774813306187e+41 best_h = 0 opt_iter = 3 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 0.1000000000000001 estimated_steps = 400.0000000000003 step_error = 2.499999999999998e-13 est_needed_step_err = 2.499999999999998e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 1.656402686869081e+33 max_value3 = 1.656402686869081e+33 value3 = 1.656402686869081e+33 best_h = 0 opt_iter = 4 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 0.1000000000000001 estimated_steps = 800.0000000000007 step_error = 1.249999999999999e-13 est_needed_step_err = 1.249999999999999e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 6.172239484265773e+24 max_value3 = 6.172239484265773e+24 value3 = 6.172239484265773e+24 best_h = 0 opt_iter = 5 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 0.1000000000000001 estimated_steps = 1600.000000000001 step_error = 6.249999999999995e-14 est_needed_step_err = 6.249999999999995e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 2.30057535835239e+16 max_value3 = 2.30057535835239e+16 value3 = 2.30057535835239e+16 best_h = 0 opt_iter = 6 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 0.1000000000000001 estimated_steps = 3200.000000000003 step_error = 3.124999999999997e-14 est_needed_step_err = 3.124999999999997e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 85795450.95080923 max_value3 = 85795450.95080923 value3 = 85795450.95080923 best_h = 0 opt_iter = 7 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 0.1000000000000001 estimated_steps = 6400.000000000005 step_error = 1.562499999999999e-14 est_needed_step_err = 1.562499999999999e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 0.3203036139898109 max_value3 = 0.3203036139898109 value3 = 0.3203036139898109 best_h = 0 opt_iter = 8 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 0.1000000000000001 estimated_steps = 12800.00000000001 step_error = 7.812499999999994e-15 est_needed_step_err = 7.812499999999994e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 1.198409406646213e-09 max_value3 = 1.198409406646213e-09 value3 = 1.198409406646213e-09 best_h = 0 opt_iter = 9 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 0.1000000000000001 estimated_steps = 25600.00000000002 step_error = 3.906249999999997e-15 est_needed_step_err = 3.906249999999997e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 4.503649142655383e-18 max_value3 = 4.503649142655383e-18 value3 = 4.503649142655383e-18 best_h = 3.90625e-06 START of Soultion t[1] = 1.5 x1[1] (analytic) = 2.000401634288267 x1[1] (numeric) = 2.000401634288267 absolute error = 0 relative error = 0 % Correct digits = 16 h = 3.90625e-06 x2[1] (analytic) = 1.004084046432682 x2[1] (numeric) = 1.004084046432682 absolute error = 0 relative error = 0 % Correct digits = 16 h = 3.90625e-06 t[1] = 1.5 x1[1] (analytic) = 2.000401634288267 x1[1] (numeric) = 2.000401634288267 absolute error = 0 relative error = 0 % Correct digits = 16 h = 3.90625e-06 x2[1] (analytic) = 1.004084046432682 x2[1] (numeric) = 1.004084046432682 absolute error = 0 relative error = 0 % Correct digits = 16 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.501003906249976 x1[1] (analytic) = 2.000401231287416 x1[1] (numeric) = 2.000401239205139 absolute error = 7.917722921746417e-09 relative error = 3.958067410631784e-07 % Correct digits = 8 h = 3.90625e-06 x2[1] (analytic) = 1.004092052966821 x2[1] (numeric) = 1.004092053163882 absolute error = 1.970612562018914e-10 relative error = 1.962581574265314e-08 % Correct digits = 9 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.502003906249953 x1[1] (analytic) = 2.000400830256678 x1[1] (numeric) = 2.000400861827021 absolute error = 3.157034322853747e-08 relative error = 1.57820086609775e-06 % Correct digits = 7 h = 3.90625e-06 x2[1] (analytic) = 1.004100044546267 x2[1] (numeric) = 1.004100045310225 absolute error = 7.639577859208657e-10 relative error = 7.608383149371167e-08 % Correct digits = 9 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.503003906249929 x1[1] (analytic) = 2.000400429626769 x1[1] (numeric) = 2.000400500618639 absolute error = 7.099187016024189e-08 relative error = 3.548882969070718e-06 % Correct digits = 7 h = 3.90625e-06 x2[1] (analytic) = 1.004108052325482 x2[1] (numeric) = 1.004108053994392 absolute error = 1.668910121210843e-09 relative error = 1.662082200561684e-07 % Correct digits = 8 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.504003906249905 x1[1] (analytic) = 2.000400029397291 x1[1] (numeric) = 2.000400155613448 absolute error = 1.26216157525505e-07 relative error = 6.3095458743586e-06 % Correct digits = 7 h = 3.90625e-06 x2[1] (analytic) = 1.004116076336697 x2[1] (numeric) = 1.00411607921673 absolute error = 2.880033767027612e-09 relative error = 2.868227921949822e-07 % Correct digits = 8 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.505003906249882 x1[1] (analytic) = 2.000399629567842 x1[1] (numeric) = 2.000399826844864 absolute error = 1.972770227176568e-07 relative error = 9.861880586344426e-06 % Correct digits = 7 h = 3.90625e-06 x2[1] (analytic) = 1.004124116612207 x2[1] (numeric) = 1.004124120977562 absolute error = 4.36535518844039e-09 relative error = 4.347425897077912e-07 % Correct digits = 8 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.506003906249858 x1[1] (analytic) = 2.000399230138022 x1[1] (numeric) = 2.000399514346276 absolute error = 2.842082538201396e-07 relative error = 1.420757664461459e-05 % Correct digits = 6 h = 3.90625e-06 x2[1] (analytic) = 1.004132173184375 x2[1] (numeric) = 1.004132179277169 absolute error = 6.092794491152631e-09 relative error = 6.067721614606503e-07 % Correct digits = 8 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.507003906249834 x1[1] (analytic) = 2.000398831107432 x1[1] (numeric) = 2.000399218151037 absolute error = 3.870436047215264e-07 relative error = 1.934832187975519e-05 % Correct digits = 6 h = 3.90625e-06 x2[1] (analytic) = 1.004140246085625 x2[1] (numeric) = 1.004140254115802 absolute error = 8.030176745776885e-09 relative error = 7.997066920761716e-07 % Correct digits = 8 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.508003906249811 x1[1] (analytic) = 2.000398432475674 x1[1] (numeric) = 2.000398938292469 absolute error = 5.058167951155212e-07 relative error = 2.528580241334858e-05 % Correct digits = 6 h = 3.90625e-06 x2[1] (analytic) = 1.004148335348451 x2[1] (numeric) = 1.00414834549368 absolute error = 1.014522910125493e-08 relative error = 1.010331715357016e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.509003906249787 x1[1] (analytic) = 2.000398034242348 x1[1] (numeric) = 2.000398674803855 absolute error = 6.405615069482451e-07 relative error = 3.202170248036952e-05 % Correct digits = 6 h = 3.90625e-06 x2[1] (analytic) = 1.004156441005406 x2[1] (numeric) = 1.004156453410987 absolute error = 1.240558034076855e-08 relative error = 1.235423070965668e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.510003906249763 x1[1] (analytic) = 2.000397636407057 x1[1] (numeric) = 2.000398427718458 absolute error = 7.913114012936262e-07 relative error = 3.955770527278327e-05 % Correct digits = 6 h = 3.90625e-06 x2[1] (analytic) = 1.004164563089115 x2[1] (numeric) = 1.004164577867874 absolute error = 1.477875977151655e-08 relative error = 1.471746794773618e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.51100390624974 x1[1] (analytic) = 2.000397238969402 x1[1] (numeric) = 2.000398197069495 absolute error = 9.58100093040315e-07 relative error = 4.789549167413994e-05 % Correct digits = 6 h = 3.90625e-06 x2[1] (analytic) = 1.004172701632262 x2[1] (numeric) = 1.004172718864461 absolute error = 1.723219944516075e-08 relative error = 1.716059340903229e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.512003906249716 x1[1] (analytic) = 2.000396841928985 x1[1] (numeric) = 2.000397982890167 absolute error = 1.14096118108975e-06 relative error = 5.703674176917415e-05 % Correct digits = 6 h = 3.90625e-06 x2[1] (analytic) = 1.004180856667602 x2[1] (numeric) = 1.004180876400834 absolute error = 1.973323215942457e-08 relative error = 1.965107383635032e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.513003906249692 x1[1] (analytic) = 2.000396445285411 x1[1] (numeric) = 2.000397785213623 absolute error = 1.339928211496755e-06 relative error = 6.698313300119753e-05 % Correct digits = 6 h = 3.90625e-06 x2[1] (analytic) = 1.004189028227954 x2[1] (numeric) = 1.004189050477045 absolute error = 2.224909101400385e-08 relative error = 2.215627774111992e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.514003906249669 x1[1] (analytic) = 2.000396049038283 x1[1] (numeric) = 2.000397604072986 absolute error = 1.555034703670799e-06 relative error = 7.773634148189819e-05 % Correct digits = 6 h = 3.90625e-06 x2[1] (analytic) = 1.004197216346201 x2[1] (numeric) = 1.004197241093112 absolute error = 2.474691163101284e-08 relative error = 2.464347762390256e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.515003906249645 x1[1] (analytic) = 2.000395653187203 x1[1] (numeric) = 2.000397439501352 absolute error = 1.786314149043733e-06 relative error = 8.92980419247374e-05 % Correct digits = 6 h = 3.90625e-06 x2[1] (analytic) = 1.004205421055294 x2[1] (numeric) = 1.004205448249023 absolute error = 2.719372926840435e-08 relative error = 2.707984710919719e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.516003906249622 x1[1] (analytic) = 2.000395257731777 x1[1] (numeric) = 2.000397291531777 absolute error = 2.033800000411645e-06 relative error = 0.0001016699071121447 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004213642388251 x2[1] (numeric) = 1.004213671944731 absolute error = 2.955647970814823e-08 relative error = 2.943246183935136e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.517003906249598 x1[1] (analytic) = 2.000394862671607 x1[1] (numeric) = 2.000397160197289 absolute error = 2.297525681260737e-06 relative error = 0.0001148536083617161 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004221880378154 x2[1] (numeric) = 1.004221912180155 absolute error = 3.180200147667733e-08 relative error = 3.166830169514116e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.518003906249574 x1[1] (analytic) = 2.000394468006301 x1[1] (numeric) = 2.00039704553088 absolute error = 2.577524579105983e-06 relative error = 0.0001288508151932094 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004230135058152 x2[1] (numeric) = 1.004230168955183 absolute error = 3.389703051581705e-08 relative error = 3.375424549857206e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.519003906249551 x1[1] (analytic) = 2.000394073735464 x1[1] (numeric) = 2.00039694756551 absolute error = 2.873830046379311e-06 relative error = 0.0001436631953729409 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004238406461463 x2[1] (numeric) = 1.004238442269668 absolute error = 3.58082046236774e-08 relative error = 3.565707544471565e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.520003906249527 x1[1] (analytic) = 2.000393679858699 x1[1] (numeric) = 2.0003968663341 absolute error = 3.1864754004296e-06 relative error = 0.0001592924149137825 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004246694621368 x2[1] (numeric) = 1.00424673212343 absolute error = 3.750206190034078e-08 relative error = 3.734347556352198e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.521003906249503 x1[1] (analytic) = 2.000393286375615 x1[1] (numeric) = 2.000396801869543 absolute error = 3.515493928851754e-06 relative error = 0.0001757401383415585 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004254999571217 x2[1] (numeric) = 1.004255038516258 absolute error = 3.894504074786198e-08 relative error = 3.878003172948126e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.52200390624948 x1[1] (analytic) = 2.000392893285817 x1[1] (numeric) = 2.000396754204701 absolute error = 3.860918883713538e-06 relative error = 0.000193008028406442 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004263321344427 x2[1] (numeric) = 1.004263361447906 absolute error = 4.010347920413437e-08 relative error = 3.993323100802592e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.523003906249456 x1[1] (analytic) = 2.000392500588912 x1[1] (numeric) = 2.000396723372395 absolute error = 4.222783482443759e-06 relative error = 0.0002110977461273515 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004271659974481 x2[1] (numeric) = 1.004271700918097 absolute error = 4.094361649720213e-08 relative error = 4.076946321301402e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.524003906249432 x1[1] (analytic) = 2.000392108284508 x1[1] (numeric) = 2.000396709405421 absolute error = 4.601120913161338e-06 relative error = 0.0002300109510583481 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.00428001549493 x2[1] (numeric) = 1.004280056926518 absolute error = 4.143158771618971e-08 relative error = 4.125501561013474e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.525003906249409 x1[1] (analytic) = 2.000391716372213 x1[1] (numeric) = 2.000396712336533 absolute error = 4.995964320464452e-06 relative error = 0.00024974930057823 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004288387939393 x2[1] (numeric) = 1.004288429472823 absolute error = 4.153343025059542e-08 relative error = 4.135607933873858e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.526003906249385 x1[1] (analytic) = 2.000391324851633 x1[1] (numeric) = 2.000396732198455 absolute error = 5.407346822305925e-06 relative error = 0.0002703144507341323 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004296777341555 x2[1] (numeric) = 1.004296818556636 absolute error = 4.12150806816669e-08 relative error = 4.103874632632612e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.527003906249361 x1[1] (analytic) = 2.000390933722379 x1[1] (numeric) = 2.000396769023878 absolute error = 5.835301498890999e-06 relative error = 0.0002917080556865212 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.00430518373517 x2[1] (numeric) = 1.004305224177544 absolute error = 4.04423745603566e-08 relative error = 4.026900907744497e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.528003906249338 x1[1] (analytic) = 2.000390542984058 x1[1] (numeric) = 2.000396822845459 absolute error = 6.279861400670939e-06 relative error = 0.000313931768108793 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004313607154058 x2[1] (numeric) = 1.004313646335105 absolute error = 3.918104662936628e-08 relative error = 3.901276090482766e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.529003906249314 x1[1] (analytic) = 2.00039015263628 x1[1] (numeric) = 2.000396893695824 absolute error = 6.741059543902139e-06 relative error = 0.0003369872389652694 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004322047632109 x2[1] (numeric) = 1.004322085028841 absolute error = 3.739673126723631e-08 relative error = 3.723579638165527e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.530003906249291 x1[1] (analytic) = 2.000389762678656 x1[1] (numeric) = 2.000396981607551 absolute error = 7.218928895547094e-06 relative error = 0.0003608761167563898 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.00433050520328 x2[1] (numeric) = 1.004330540258241 absolute error = 3.505496026789956e-08 relative error = 3.490380914080102e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.531003906249267 x1[1] (analytic) = 2.000389373110794 x1[1] (numeric) = 2.0003970866132 absolute error = 7.713502406136996e-06 relative error = 0.0003856000491615177 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004338979901596 x2[1] (numeric) = 1.004339012022762 absolute error = 3.21211652831721e-08 relative error = 3.19823943170256e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.532003906249243 x1[1] (analytic) = 2.000388983932304 x1[1] (numeric) = 2.00039720874529 absolute error = 8.224812986235008e-06 relative error = 0.0004111606818623306 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004347471761151 x2[1] (numeric) = 1.004347500321828 absolute error = 2.856067649048555e-08 relative error = 2.843704723067964e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.53300390624922 x1[1] (analytic) = 2.000388595142799 x1[1] (numeric) = 2.000397348036308 absolute error = 8.752893508656712e-06 relative error = 0.0004375596586538167 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004355980816107 x2[1] (numeric) = 1.004356005154829 absolute error = 2.433872237084245e-08 relative error = 2.423316317693015e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.534003906249196 x1[1] (analytic) = 2.000388206741889 x1[1] (numeric) = 2.000397504518701 absolute error = 9.297776811578728e-06 relative error = 0.0004647986215996736 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004364507100694 x2[1] (numeric) = 1.004364526521123 absolute error = 1.942042882063788e-08 relative error = 1.933603655180823e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.535003906249172 x1[1] (analytic) = 2.000387818729186 x1[1] (numeric) = 2.000397678224892 absolute error = 9.85949570564415e-06 relative error = 0.0004928792113875062 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004373050649212 x2[1] (numeric) = 1.004373064420034 absolute error = 1.377082159415011e-08 relative error = 1.371086329451875e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.536003906249149 x1[1] (analytic) = 2.000387431104302 x1[1] (numeric) = 2.000397869187263 absolute error = 1.043808296152804e-05 relative error = 0.0005218030667072208 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004381611496029 x2[1] (numeric) = 1.004381618850852 absolute error = 7.354822750826884e-09 relative error = 7.322737360625168e-07 % Correct digits = 8 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.537003906249125 x1[1] (analytic) = 2.000387043866848 x1[1] (numeric) = 2.000398077438157 absolute error = 1.103357130860516e-05 relative error = 0.0005515718241844197 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004390189675582 x2[1] (numeric) = 1.00439018981284 absolute error = 1.372584268466426e-10 relative error = 1.366584702415075e-08 % Correct digits = 9 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.538003906249101 x1[1] (analytic) = 2.000386657016439 x1[1] (numeric) = 2.000398303009892 absolute error = 1.164599345315764e-05 relative error = 0.0005821871192906051 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004398785222378 x2[1] (numeric) = 1.004398777305216 absolute error = 7.917161592985167e-09 relative error = 7.882488220286206e-07 % Correct digits = 8 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.539003906249078 x1[1] (analytic) = 2.000386270552687 x1[1] (numeric) = 2.000398545934747 absolute error = 1.227538206061141e-05 relative error = 0.0006136505854551702 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004407398170992 x2[1] (numeric) = 1.004407381327174 absolute error = 1.684381767397269e-08 relative error = 1.676990602084871e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.540003906249054 x1[1] (analytic) = 2.000385884475205 x1[1] (numeric) = 2.000398806244963 absolute error = 1.292176975864479e-05 relative error = 0.0006459638542207957 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004416028556068 x2[1] (numeric) = 1.004416001877873 absolute error = 2.667819498647361e-08 relative error = 2.656090128791128e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.54100390624903 x1[1] (analytic) = 2.000385498783607 x1[1] (numeric) = 2.000399083972753 absolute error = 1.358518914562623e-05 relative error = 0.0006791285556652506 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004424676412323 x2[1] (numeric) = 1.004424638956441 absolute error = 3.74558826177207e-08 relative error = 3.729088252939816e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.542003906249007 x1[1] (analytic) = 2.000385113477509 x1[1] (numeric) = 2.000399379150295 absolute error = 1.426567278572932e-05 relative error = 0.0007131463181571869 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.00443334177454 x2[1] (numeric) = 1.004433292561968 absolute error = 4.921257223955422e-08 relative error = 4.899535906744194e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.543003906248983 x1[1] (analytic) = 2.000384728556524 x1[1] (numeric) = 2.000399691809721 absolute error = 1.496325319738645e-05 relative error = 0.0007480187677789323 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004442024677573 x2[1] (numeric) = 1.004441962693514 absolute error = 6.198405921864492e-08 relative error = 6.170994213283923e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.544003906248959 x1[1] (analytic) = 2.000384344020268 x1[1] (numeric) = 2.000400021983141 absolute error = 1.567796287282874e-05 relative error = 0.0007837475293032935 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004450725156347 x2[1] (numeric) = 1.004450649350107 absolute error = 7.580623972991418e-08 relative error = 7.547034198030436e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.545003906248936 x1[1] (analytic) = 2.000383959868356 x1[1] (numeric) = 2.00040036970262 absolute error = 1.640983426476339e-05 relative error = 0.0008203342255275488 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004459443245854 x2[1] (numeric) = 1.00445935253074 absolute error = 9.071511408720312e-08 relative error = 9.031237119346731e-06 % Correct digits = 7 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.546003906248912 x1[1] (analytic) = 2.000383576100403 x1[1] (numeric) = 2.0004007350002 absolute error = 1.715889979658769e-05 relative error = 0.0008577804777840493 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004468178981161 x2[1] (numeric) = 1.004468072234372 absolute error = 1.067467889637186e-07 relative error = 1.062719468843628e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.547003906248889 x1[1] (analytic) = 2.000383192716027 x1[1] (numeric) = 2.00040111790788 absolute error = 1.792519185261909e-05 relative error = 0.0008960879054518102 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004476932397402 x2[1] (numeric) = 1.004476808459931 absolute error = 1.239374702866058e-07 relative error = 1.233850836084431e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.548003906248865 x1[1] (analytic) = 2.000382809714843 x1[1] (numeric) = 2.00040151845762 absolute error = 1.870874277631884e-05 relative error = 0.000935258125867708 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004485703529781 x2[1] (numeric) = 1.004485561206311 absolute error = 1.423234705644205e-07 relative error = 1.416879006483549e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.549003906248841 x1[1] (analytic) = 2.000382427096469 x1[1] (numeric) = 2.000401936681352 absolute error = 1.950958488272647e-05 relative error = 0.0009752927549480823 % Correct digits = 5 h = 3.90625e-06 x2[1] (analytic) = 1.004494492413576 x2[1] (numeric) = 1.004494330472372 absolute error = 1.619412040021473e-07 relative error = 1.612166171394716e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.550003906248818 x1[1] (analytic) = 2.000382044860523 x1[1] (numeric) = 2.000402372610972 absolute error = 2.032775044913393e-05 relative error = 0.001016193406722529 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004503299084133 x2[1] (numeric) = 1.004503116256944 absolute error = 1.828271891657351e-07 relative error = 1.820075547112985e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.551003906248794 x1[1] (analytic) = 2.000381663006621 x1[1] (numeric) = 2.000402826278335 absolute error = 2.116327171419741e-05 relative error = 0.001057961693289495 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004512123576869 x2[1] (numeric) = 1.004511918558821 absolute error = 2.05018048093919e-07 relative error = 2.04097136591931e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.55200390624877 x1[1] (analytic) = 2.000381281534382 x1[1] (numeric) = 2.000403297715266 absolute error = 2.20161808832664e-05 relative error = 0.00110059922508268 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004520965927275 x2[1] (numeric) = 1.004520737376766 absolute error = 2.285505089627549e-07 relative error = 2.27521890249229e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.553003906248747 x1[1] (analytic) = 2.000380900443425 x1[1] (numeric) = 2.00040378695355 absolute error = 2.288651012438692e-05 relative error = 0.00114410761067123 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004529826170909 x2[1] (numeric) = 1.004529572709507 absolute error = 2.534614020888171e-07 relative error = 2.523184434004985e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.554003906248723 x1[1] (analytic) = 2.000380519733369 x1[1] (numeric) = 2.000404294024941 absolute error = 2.377429157274236e-05 relative error = 0.001188488456981737 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004538704343403 x2[1] (numeric) = 1.00453842455574 absolute error = 2.797876637039565e-07 relative error = 2.785235277587777e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.555003906248699 x1[1] (analytic) = 2.000380139403832 x1[1] (numeric) = 2.000404818961164 absolute error = 2.467955733198579e-05 relative error = 0.001233743369364834 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004547600480462 x2[1] (numeric) = 1.004547292914127 absolute error = 3.075663346230328e-07 relative error = 3.061739776949624e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.556003906248676 x1[1] (analytic) = 2.000379759454434 x1[1] (numeric) = 2.00040536179389 absolute error = 2.56023394560323e-05 relative error = 0.001279873950684987 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004556514617858 x2[1] (numeric) = 1.004556177783298 absolute error = 3.368345600218703e-07 relative error = 3.353067300051357e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.557003906248652 x1[1] (analytic) = 2.000379379884796 x1[1] (numeric) = 2.000405922554765 absolute error = 2.654266996904298e-05 relative error = 0.001326881802319498 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004565446791439 x2[1] (numeric) = 1.004565079161851 absolute error = 3.676295885490788e-07 relative error = 3.659588230147473e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.558003906248628 x1[1] (analytic) = 2.000379000694538 x1[1] (numeric) = 2.000406501275398 absolute error = 2.750058085965179e-05 relative error = 0.001374768523869901 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004574397037123 x2[1] (numeric) = 1.004573997048347 absolute error = 3.999887763228571e-07 relative error = 3.981674005455225e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.559003906248605 x1[1] (analytic) = 2.000378621883281 x1[1] (numeric) = 2.000407097987365 absolute error = 2.847610408451828e-05 relative error = 0.001423535713339563 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004583365390901 x2[1] (numeric) = 1.00458293144132 absolute error = 4.339495816019223e-07 relative error = 4.319697065987797e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.560003906248581 x1[1] (analytic) = 2.000378243450645 x1[1] (numeric) = 2.000407712722204 absolute error = 2.946927155811352e-05 relative error = 0.001473184966623069 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004592351888836 x2[1] (numeric) = 1.004591882339264 absolute error = 4.695495725570709e-07 relative error = 4.674030930797183e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.561003906248557 x1[1] (analytic) = 2.000377865396254 x1[1] (numeric) = 2.000408345511409 absolute error = 3.048011515538462e-05 relative error = 0.001523717877639425 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004601356567063 x2[1] (numeric) = 1.004600849740646 absolute error = 5.068264172791714e-07 relative error = 5.045050098390324e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.562003906248534 x1[1] (analytic) = 2.000377487719727 x1[1] (numeric) = 2.000408996386456 absolute error = 3.150866672863017e-05 relative error = 0.001575136039175664 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004610379461789 x2[1] (numeric) = 1.004609833643896 absolute error = 5.458178931050384e-07 relative error = 5.433130139442272e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.56300390624851 x1[1] (analytic) = 2.000377110420688 x1[1] (numeric) = 2.000409665378765 absolute error = 3.255495807641395e-05 relative error = 0.001627441041332826 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004619420609295 x2[1] (numeric) = 1.004618834047413 absolute error = 5.865618826206287e-07 relative error = 5.838647656889637e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.564003906248487 x1[1] (analytic) = 2.00037673349876 x1[1] (numeric) = 2.000410352519737 absolute error = 3.361902097731573e-05 relative error = 0.001680634473213171 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004628480045935 x2[1] (numeric) = 1.004627850949561 absolute error = 6.290963745492206e-07 relative error = 6.261980294650378e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.565003906248463 x1[1] (analytic) = 2.000376356953565 x1[1] (numeric) = 2.000411057840723 absolute error = 3.470088715751274e-05 relative error = 0.001734717921299559 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004637557808134 x2[1] (numeric) = 1.004636884348673 absolute error = 6.734594608648337e-07 relative error = 6.703506708769205e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.566003906248439 x1[1] (analytic) = 2.000375980784728 x1[1] (numeric) = 2.000411781373043 absolute error = 3.580058831520461e-05 relative error = 0.001789692970676462 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004646653932392 x2[1] (numeric) = 1.00464593424305 absolute error = 7.196893416772099e-07 relative error = 7.163606615920124e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.567003906248416 x1[1] (analytic) = 2.00037560499187 x1[1] (numeric) = 2.000412523147985 absolute error = 3.691815611439608e-05 relative error = 0.001845561204719157 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004655768455282 x2[1] (numeric) = 1.004655000630959 absolute error = 7.678243230113679e-07 relative error = 7.642660771180796e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.568003906248392 x1[1] (analytic) = 2.000375229574618 x1[1] (numeric) = 2.000413283196796 absolute error = 3.805362217779162e-05 relative error = 0.001902324204738516 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004664901413449 x2[1] (numeric) = 1.004664083510629 absolute error = 8.179028194721383e-07 relative error = 8.141050994430505e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.569003906248368 x1[1] (analytic) = 2.000374854532596 x1[1] (numeric) = 2.000414061550683 absolute error = 3.920701808679539e-05 relative error = 0.001959983549981007 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004674052843613 x2[1] (numeric) = 1.004673182880264 absolute error = 8.699633484710034e-07 relative error = 8.659160112761683e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.570003906248345 x1[1] (analytic) = 2.000374479865429 x1[1] (numeric) = 2.000414858240825 absolute error = 4.037837539616618e-05 relative error = 0.002018540818361298 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004683222782567 x2[1] (numeric) = 1.004682298738033 absolute error = 9.240445340008563e-07 relative error = 9.197371997928121e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.571003906248321 x1[1] (analytic) = 2.000374105572741 x1[1] (numeric) = 2.000415673298358 absolute error = 4.156772561714206e-05 relative error = 0.002077997585618642 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004692411267178 x2[1] (numeric) = 1.004691431082064 absolute error = 9.801851141855167e-07 relative error = 9.756071641361841e-05 % Correct digits = 6 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.572003906248297 x1[1] (analytic) = 2.000373731654158 x1[1] (numeric) = 2.000416506754383 absolute error = 4.277510022498987e-05 relative error = 0.002138355425694282 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004701618334388 x2[1] (numeric) = 1.004700579910463 absolute error = 1.03842392529252e-06 relative error = 0.0001033564499491935 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.573003906248274 x1[1] (analytic) = 2.000373358109308 x1[1] (numeric) = 2.000417358639965 absolute error = 4.400053065722886e-05 relative error = 0.002199615910642643 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004710844021212 x2[1] (numeric) = 1.004709745221296 absolute error = 1.098799916166016e-06 relative error = 0.0001093647911441092 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.57400390624825 x1[1] (analytic) = 2.000372984937815 x1[1] (numeric) = 2.000418228986135 absolute error = 4.524404831940387e-05 relative error = 0.002261780610919936 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004720088364739 x2[1] (numeric) = 1.004718927012598 absolute error = 1.161352140899297e-06 relative error = 0.0001155896208653983 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.575003906248226 x1[1] (analytic) = 2.000372612139308 x1[1] (numeric) = 2.000419117823877 absolute error = 4.650568456909809e-05 relative error = 0.002324851094584942 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004729351402133 x2[1] (numeric) = 1.004728125282374 absolute error = 1.226119759056843e-06 relative error = 0.0001220348303098493 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.576003906248203 x1[1] (analytic) = 2.000372239713412 x1[1] (numeric) = 2.000420025184146 absolute error = 4.778547073369666e-05 relative error = 0.002388828928187023 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004738633170633 x2[1] (numeric) = 1.004737340028592 absolute error = 1.293142041003392e-06 relative error = 0.0001287043215331186 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.577003906248179 x1[1] (analytic) = 2.000371867659757 x1[1] (numeric) = 2.000420951097863 absolute error = 4.908343810594573e-05 relative error = 0.002453715676544114 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004747933707552 x2[1] (numeric) = 1.004746571249189 absolute error = 1.362458363018959e-06 relative error = 0.0001356020069622282 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.578003906248155 x1[1] (analytic) = 2.000371495977969 x1[1] (numeric) = 2.000421895595901 absolute error = 5.039961793196213e-05 relative error = 0.002519512902143313 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004757253050278 x2[1] (numeric) = 1.004755818942067 absolute error = 1.434108211073593e-06 relative error = 0.0001427318097699594 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.579003906248132 x1[1] (analytic) = 2.000371124667677 x1[1] (numeric) = 2.00042285870911 absolute error = 5.173404143254956e-05 relative error = 0.002586222166206492 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004766591236275 x2[1] (numeric) = 1.004765083105097 absolute error = 1.508131178384886e-06 relative error = 0.0001500976636304423 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.580003906248108 x1[1] (analytic) = 2.00037075372851 x1[1] (numeric) = 2.000423840468291 absolute error = 5.308673978055012e-05 relative error = 0.002653845027558078 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004775948303081 x2[1] (numeric) = 1.004774363736116 absolute error = 1.584566965195933e-06 relative error = 0.0001577035126957442 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.581003906248085 x1[1] (analytic) = 2.000370383160096 x1[1] (numeric) = 2.000424840904209 absolute error = 5.445774411239057e-05 relative error = 0.002722383043202262 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004785324288309 x2[1] (numeric) = 1.004783660832929 absolute error = 1.663455380551682e-06 relative error = 0.0001655533117713388 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.582003906248061 x1[1] (analytic) = 2.000370012962066 x1[1] (numeric) = 2.000425860047604 absolute error = 5.584708553740825e-05 relative error = 0.002791837768789193 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004794719229649 x2[1] (numeric) = 1.004792974393306 absolute error = 1.744836343409162e-06 relative error = 0.0001736510264252667 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.583003906248037 x1[1] (analytic) = 2.000369643134049 x1[1] (numeric) = 2.000426897929159 absolute error = 5.725479510942932e-05 relative error = 0.002862210757194167 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004804133164866 x2[1] (numeric) = 1.004802304414987 absolute error = 1.828749879084768e-06 relative error = 0.000182000632633217 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.584003906248014 x1[1] (analytic) = 2.000369273675675 x1[1] (numeric) = 2.000427954579532 absolute error = 5.868090385741098e-05 relative error = 0.002933503560049437 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.0048135661318 x2[1] (numeric) = 1.00481165089568 absolute error = 1.915236120142438e-06 relative error = 0.0001906061168655857 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.58500390624799 x1[1] (analytic) = 2.000368904586574 x1[1] (numeric) = 2.000429030029351 absolute error = 6.012544277655962e-05 relative error = 0.003005717727300206 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004823018168369 x2[1] (numeric) = 1.004821013833053 absolute error = 2.004335315497485e-06 relative error = 0.0001994714769921441 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.586003906247966 x1[1] (analytic) = 2.000368535866379 x1[1] (numeric) = 2.000430124309186 absolute error = 6.158844280701459e-05 relative error = 0.003078854806139012 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004832489312564 x2[1] (numeric) = 1.004830393224748 absolute error = 2.096087815983694e-06 relative error = 0.0002086007208442962 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.587003906247943 x1[1] (analytic) = 2.000368167514719 x1[1] (numeric) = 2.000431237449579 absolute error = 6.306993485960533e-05 relative error = 0.003152916342293337 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004841979602454 x2[1] (numeric) = 1.004839789068371 absolute error = 2.190534083679196e-06 relative error = 0.0002179978671418403 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.588003906247919 x1[1] (analytic) = 2.000367799531227 x1[1] (numeric) = 2.00043236948104 absolute error = 6.456994981274278e-05 relative error = 0.003227903879870208 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004851489076186 x2[1] (numeric) = 1.004849201361497 absolute error = 2.287714689686027e-06 relative error = 0.0002276669452706136 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.589003906247895 x1[1] (analytic) = 2.000367431915534 x1[1] (numeric) = 2.000433520434036 absolute error = 6.608851850220532e-05 relative error = 0.003303818960845586 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004861017771981 x2[1] (numeric) = 1.004858630101665 absolute error = 2.387670315462387e-06 relative error = 0.0002376119954136969 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.590003906247872 x1[1] (analytic) = 2.000367064667273 x1[1] (numeric) = 2.000434690338995 absolute error = 6.762567172202694e-05 relative error = 0.003380663125108757 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004870565728137 x2[1] (numeric) = 1.004868075286385 absolute error = 2.490441752156514e-06 relative error = 0.0002478370684837325 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.591003906247848 x1[1] (analytic) = 2.000366697786077 x1[1] (numeric) = 2.000435879226311 absolute error = 6.91814402342672e-05 relative error = 0.003458437910950745 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.00488013298303 x2[1] (numeric) = 1.004877536913131 absolute error = 2.596069899496456e-06 relative error = 0.0002583462260110477 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.592003906247824 x1[1] (analytic) = 2.000366331271579 x1[1] (numeric) = 2.000437087126343 absolute error = 7.075585476457036e-05 relative error = 0.003537144854842302 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004889719575113 x2[1] (numeric) = 1.004887014979345 absolute error = 2.704595768232565e-06 relative error = 0.0002691435403853192 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.593003906247801 x1[1] (analytic) = 2.000365965123412 x1[1] (numeric) = 2.000438314069398 absolute error = 7.234894598617814e-05 relative error = 0.00361678549063469 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004899325542915 x2[1] (numeric) = 1.004896509482437 absolute error = 2.816060478361138e-06 relative error = 0.0002802330946773907 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.594003906247777 x1[1] (analytic) = 2.00036559934121 x1[1] (numeric) = 2.000439560085761 absolute error = 7.396074455101598e-05 relative error = 0.003697361351113708 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004908950925043 x2[1] (numeric) = 1.004906020419781 absolute error = 2.930505261566907e-06 relative error = 0.0002916189828809174 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.595003906247753 x1[1] (analytic) = 2.000365233924608 x1[1] (numeric) = 2.000440825205667 absolute error = 7.559128105905089e-05 relative error = 0.003778873966467859 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004918595760181 x2[1] (numeric) = 1.004915547788726 absolute error = 3.047971455227838e-06 relative error = 0.0003033053093143498 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.59600390624773 x1[1] (analytic) = 2.000364868873239 x1[1] (numeric) = 2.000442109459318 absolute error = 7.724058607916362e-05 relative error = 0.00386132486533177 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004928260087092 x2[1] (numeric) = 1.004925091586575 absolute error = 3.168500516848027e-06 relative error = 0.0003152961900557388 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.597003906247706 x1[1] (analytic) = 2.00036450418674 x1[1] (numeric) = 2.000443412876885 absolute error = 7.890869014515189e-05 relative error = 0.003944715574586377 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004937943944615 x2[1] (numeric) = 1.004934651810611 absolute error = 3.292134004739822e-06 relative error = 0.0003275957510189564 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.598003906247683 x1[1] (analytic) = 2.000364139864744 x1[1] (numeric) = 2.000444735488486 absolute error = 8.059562374196361e-05 relative error = 0.004029047618670725 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004947647371669 x2[1] (numeric) = 1.004944228458076 absolute error = 3.418913592678763e-06 relative error = 0.0003402081294105776 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.599003906247659 x1[1] (analytic) = 2.000363775906889 x1[1] (numeric) = 2.000446077324205 absolute error = 8.230141731679907e-05 relative error = 0.004114322520136956 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004957370407249 x2[1] (numeric) = 1.004953821526184 absolute error = 3.548881064574516e-06 relative error = 0.0003531374731981287 % Correct digits = 5 h = 3.90625e-06 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 1.600003906247635 x1[1] (analytic) = 2.000363412312809 x1[1] (numeric) = 2.000447438414097 absolute error = 8.402610128754873e-05 relative error = 0.004200541800072128 % Correct digits = 4 h = 3.90625e-06 x2[1] (analytic) = 1.004967113090428 x2[1] (numeric) = 1.004963431012113 absolute error = 3.68207831535905e-06 relative error = 0.0003663879411970102 % Correct digits = 5 h = 3.90625e-06 Finished! diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; Iterations = 25601 Total Elapsed Time = 14 Seconds Elapsed Time(since restart) = 14 Seconds Time to Timeout = 1 Minutes 46 Seconds Percent Done = 100 %