##############ECHO OF PROBLEM################# ##############temp/lin_sinhpostode.ode################# diff ( y , x , 1 ) = sinh ( 2.0 * x + 3.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.1); x_end=c(2.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=0.000000001; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(20.0); glob_subiter_method=3; glob_max_iter=1000; glob_upper_ratio_limit=c(1.11); glob_lower_ratio_limit=c(0.99); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(cosh(c(2.0)*c(x)+c(3.0))/c(2.0)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 6.14332310027193 y[1] (numeric) = 6.14332310027193 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 SETTING H FOR POLE NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.56 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.19999944784701 y[1] (closed_form) = 7.499360066173765 y[1] (numeric) = 7.499360066165517 absolute error = 8.248512983755063e-12 relative error = 1.099895579218871e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.02499986196175249 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.54 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2999988956940199 y[1] (closed_form) = 9.156369348815947 y[1] (numeric) = 9.15636934879762 absolute error = 1.832667351209238e-11 relative error = 2.00152187116199e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.02499986196175249 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.53 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3999983435410298 y[1] (closed_form) = 11.18085181203972 y[1] (numeric) = 11.18085181200908 absolute error = 3.064748455017252e-11 relative error = 2.741068843893522e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.02499986196175249 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.52 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4999977913880397 y[1] (closed_form) = 13.65405614530393 y[1] (numeric) = 13.65405614525825 absolute error = 4.568612155253504e-11 relative error = 3.345974343913033e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.02499986196175249 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.51 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5999972392350498 y[1] (closed_form) = 16.67523962274753 y[1] (numeric) = 16.67523962268346 absolute error = 6.406963848348823e-11 relative error = 3.842201967286134e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.02499986196175249 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.51 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6999966870820599 y[1] (closed_form) = 20.36565160197972 y[1] (numeric) = 20.3656516018932 absolute error = 8.65263416471862e-11 relative error = 4.248640963629912e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.02499986196175249 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.51 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.79999613492907 y[1] (closed_form) = 24.8733996326201 y[1] (numeric) = 24.87339963250614 absolute error = 1.139568439612049e-10 relative error = 4.581474412197226e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.02499986196175249 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.89999558277608 y[1] (closed_form) = 30.37939346644642 y[1] (numeric) = 30.37939346629895 absolute error = 1.474660393796512e-10 relative error = 4.854146925037368e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.02499986196175249 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9999950306230901 y[1] (closed_form) = 37.10460552050522 y[1] (numeric) = 37.10460552031683 absolute error = 1.883861955320754e-10 relative error = 5.077164758643425e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.02499986196175249 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.0999944784701 y[1] (closed_form) = 45.31893917783444 y[1] (numeric) = 45.31893917759611 absolute error = 2.383302444286528e-10 relative error = 5.258954617040561e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.02499986196175249 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.19999392631711 y[1] (closed_form) = 55.35206083790144 y[1] (numeric) = 55.3520608376021 absolute error = 2.993445491483726e-10 relative error = 5.408010914444601e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.02499986196175249 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.299993374164119 y[1] (closed_form) = 67.60663044015739 y[1] (numeric) = 67.60663043978353 absolute error = 3.738591658475343e-10 relative error = 5.52991863983606e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.02499986196175249 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.399992822011129 y[1] (closed_form) = 82.57446144219089 y[1] (numeric) = 82.57446144172602 absolute error = 4.648796902984031e-10 relative error = 5.629824066413781e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.02499986196175249 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.499992269858138 y[1] (closed_form) = 100.8562588019596 y[1] (numeric) = 100.8562588013835 absolute error = 5.760654175901436e-10 relative error = 5.711746840831171e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.02499986196175249 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.599991717705148 y[1] (closed_form) = 123.1857271098545 y[1] (numeric) = 123.1857271091427 absolute error = 7.118217126844684e-10 relative error = 5.778443082530823e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.02499986196175249 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.699991165552158 y[1] (closed_form) = 150.4590164038663 y[1] (numeric) = 150.4590164029886 absolute error = 8.777192306297366e-10 relative error = 5.833610052811577e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.02499986196175249 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.799990613399167 y[1] (closed_form) = 183.7706874187133 y[1] (numeric) = 183.7706874176331 absolute error = 1.080252332030796e-09 relative error = 5.878262454171969e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.02499986196175249 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.899990061246177 y[1] (closed_form) = 224.4576396646688 y[1] (numeric) = 224.4576396633412 absolute error = 1.327663312622462e-09 relative error = 5.914983845530679e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.02499986196175249 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.999989509093187 y[1] (closed_form) = 274.1527653045993 y[1] (numeric) = 274.1527653029695 absolute error = 1.629814505577087e-09 relative error = 5.944913609630276e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.02499986196175249 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sinh ( 2.0 * x + 3.0 ) ; Iterations = 77 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 102.6 %