##############ECHO OF PROBLEM################# ##############temp/lin_coshpostode.ode################# diff ( y , x , 1 ) = cosh ( 2.0 * x + 3.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* 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=c(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(sinh(c(2.0)*c(x)+c(3.0))/c(2)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 6.122941998282746 y[1] (numeric) = 6.122941998282746 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 = 12.46 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.19999944784701 y[1] (closed_form) = 7.482673412766441 y[1] (numeric) = 7.482673412758169 absolute error = 8.271605622667266e-12 relative error = 1.10543453741477e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0249998619617525 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.47 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2999988956940199 y[1] (closed_form) = 9.142707457418519 y[1] (numeric) = 9.142707457400148 absolute error = 1.837108243307739e-11 relative error = 2.00937003821235e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0249998619617525 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.48 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.39999834354103 y[1] (closed_form) = 11.16966638905531 y[1] (numeric) = 11.16966638902461 absolute error = 3.070610432587273e-11 relative error = 2.749061901791476e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0249998619617525 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.49 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4999977913880401 y[1] (closed_form) = 13.64489828540735 y[1] (numeric) = 13.64489828536158 absolute error = 4.576961032398685e-11 relative error = 3.354338696165699e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0249998619617525 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.49 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5999972392350502 y[1] (closed_form) = 16.66774179293792 y[1] (numeric) = 16.66774179287376 absolute error = 6.416200903913705e-11 relative error = 3.849472222225227e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0249998619617525 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.49 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6999966870820603 y[1] (closed_form) = 20.35951289135426 y[1] (numeric) = 20.35951289126762 absolute error = 8.663647577122902e-11 relative error = 4.255331462670676e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0249998619617525 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7999961349290704 y[1] (closed_form) = 24.8683736758966 y[1] (numeric) = 24.86837367578253 absolute error = 1.140705307989265e-10 relative error = 4.586971881860055e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0249998619617525 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8999955827760805 y[1] (closed_form) = 30.37527855656914 y[1] (numeric) = 30.37527855642156 absolute error = 1.47576173503694e-10 relative error = 4.858430293202309e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0249998619617525 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9999950306230906 y[1] (closed_form) = 37.10123651352215 y[1] (numeric) = 37.10123651333364 absolute error = 1.885069877971546e-10 relative error = 5.080881542275556e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0249998619617525 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.0999944784701 y[1] (closed_form) = 45.3161808651641 y[1] (numeric) = 45.3161808649256 absolute error = 2.385007746852352e-10 relative error = 5.263037840608892e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0249998619617525 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.19999392631711 y[1] (closed_form) = 55.34980251999779 y[1] (numeric) = 55.34980251969827 absolute error = 2.995221848323126e-10 relative error = 5.411440894013954e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0249998619617525 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.29999337416412 y[1] (closed_form) = 67.60478148379767 y[1] (numeric) = 67.60478148342362 absolute error = 3.740439069588319e-10 relative error = 5.532802543685113e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0249998619617525 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.399992822011129 y[1] (closed_form) = 82.57294764308645 y[1] (numeric) = 82.57294764262137 absolute error = 4.65078642264416e-10 relative error = 5.632336685795367e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0249998619617525 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.499992269858139 y[1] (closed_form) = 100.8550194067102 y[1] (numeric) = 100.8550194061339 absolute error = 5.76235947846726e-10 relative error = 5.713507877312327e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0249998619617525 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.599991717705149 y[1] (closed_form) = 123.1847123777281 y[1] (numeric) = 123.184712377016 absolute error = 7.120490863599116e-10 relative error = 5.780336476952726e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0249998619617525 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.699991165552158 y[1] (closed_form) = 150.4581856105509 y[1] (numeric) = 150.458185609673 absolute error = 8.77889760886319e-10 relative error = 5.834775670887506e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0249998619617525 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.799990613399168 y[1] (closed_form) = 183.7700072219255 y[1] (numeric) = 183.770007220845 absolute error = 1.080451283996808e-09 relative error = 5.879366825577947e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0249998619617525 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.899990061246178 y[1] (closed_form) = 224.4570827660256 y[1] (numeric) = 224.4570827646978 absolute error = 1.327890686297906e-09 relative error = 5.916011515137174e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0249998619617525 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.999989509093187 y[1] (closed_form) = 274.1523093540504 y[1] (numeric) = 274.1523093524204 absolute error = 1.630041879252531e-09 relative error = 5.945752866693654e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0249998619617525 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = cosh ( 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 %