##############ECHO OF PROBLEM################# ##############temp/cosh_sqrtpostode.ode################# diff ( y , x , 1 ) = cosh ( sqrt ( 0.1 * x + 0.2 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-1.9); x_end=c(-1.8); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.01; glob_upper_ratio_limit=c(1.001); glob_lower_ratio_limit=c(0.999); glob_type_given_pole=1; array_given_rad_poles[1][1]=c(-2.0); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(0.5); array_given_ord_poles[1][2]=c(0.0); /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=true; glob_h=c(0.001); glob_display_interval=c(0.01); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(c(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * sinh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * cosh( sqrt(c(0.1) * c(x) + c(0.2)))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (closed_form) = -19.89974986107638 y[1] (numeric) = -19.89974986107638 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.890000000000001 y[1] (closed_form) = -19.88969731508805 y[1] (numeric) = -19.88969756592337 absolute error = 2.508353240671113e-07 relative error = 1.261131932243288e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 Radius of convergence (given) for eq 1 = 0.11 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.880000000000002 y[1] (closed_form) = -19.87963975992799 y[1] (numeric) = -19.87964026160569 absolute error = 5.01677700270875e-07 relative error = 2.523575408454445e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 Radius of convergence (given) for eq 1 = 0.12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.870000000000003 y[1] (closed_form) = -19.86957719476193 y[1] (numeric) = -19.86957794729463 absolute error = 7.525327028190532e-07 relative error = 3.787361429197587e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 Radius of convergence (given) for eq 1 = 0.13 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.860000000000004 y[1] (closed_form) = -19.85950961875548 y[1] (numeric) = -19.85951062216013 absolute error = 1.003404655364193e-06 relative error = 5.052514763086444e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 Radius of convergence (given) for eq 1 = 0.14 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.850000000000005 y[1] (closed_form) = -19.84943703107419 y[1] (numeric) = -19.84943828537116 absolute error = 1.254296968511426e-06 relative error = 6.319055631390606e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 Radius of convergence (given) for eq 1 = 0.15 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.840000000000007 y[1] (closed_form) = -19.83935943088351 y[1] (numeric) = -19.83936093609594 absolute error = 1.50521243114099e-06 relative error = 7.58700116495625e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 Radius of convergence (given) for eq 1 = 0.16 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.830000000000008 y[1] (closed_form) = -19.82927681734882 y[1] (numeric) = -19.82927857350212 absolute error = 1.756153295673357e-06 relative error = 8.856365826397068e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 Radius of convergence (given) for eq 1 = 0.17 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.820000000000009 y[1] (closed_form) = -19.81918918963542 y[1] (numeric) = -19.81919119675684 absolute error = 2.007121427283209e-06 relative error = 1.012716215622407e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 Radius of convergence (given) for eq 1 = 0.18 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.81000000000001 y[1] (closed_form) = -19.80909654690849 y[1] (numeric) = -19.8090988050269 absolute error = 2.258118406928133e-06 relative error = 1.139940128809432e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 Radius of convergence (given) for eq 1 = 0.19 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.800000000000011 y[1] (closed_form) = -19.79899888833318 y[1] (numeric) = -19.79900139747874 absolute error = 2.509145556217618e-06 relative error = 1.267309307086312e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 Radius of convergence (given) for eq 1 = 0.2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = cosh ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 101 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 102 %