##############ECHO OF PROBLEM################# ##############temp/cos_sqrt_linpostode.ode################# diff ( y , x , 1 ) = cos ( sqrt ( 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(-1.4); x_end=c(-1.3); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.0001; 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(-1.5); 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(cos(sqrt(c(2.0)*c(x)+c(3.0)))+sqrt(c(2.0)*c(x)+c(3.0))*sin(sqrt(c(2.0)*c(x)+c(3.0)))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -1.4 y[1] (closed_form) = 1.095055278569961 y[1] (numeric) = 1.095055278569961 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] = -1.390000000000001 y[1] (closed_form) = 1.104023539025582 y[1] (numeric) = 1.104028373805316 absolute error = 4.834779734119721e-06 relative error = 0.0004379236097073554 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 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] = -1.380000000000002 y[1] (closed_form) = 1.112895425970474 y[1] (numeric) = 1.112905078533575 absolute error = 9.652563101703038e-06 relative error = 0.0008673378357437091 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 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] = -1.370000000000003 y[1] (closed_form) = 1.121671265134129 y[1] (numeric) = 1.121685718628241 absolute error = 1.445349411111074e-05 relative error = 0.001288567743543149 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 5 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] = -1.360000000000004 y[1] (closed_form) = 1.130351381590728 y[1] (numeric) = 1.130370619282664 absolute error = 1.923769193656888e-05 relative error = 0.001701921389214029 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 5 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] = -1.350000000000005 y[1] (closed_form) = 1.138936099760073 y[1] (numeric) = 1.138960105017846 absolute error = 2.400525777357387e-05 relative error = 0.002107691360264268 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 5 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] = -1.340000000000007 y[1] (closed_form) = 1.147425743408531 y[1] (numeric) = 1.147454499688013 absolute error = 2.87562794827334e-05 relative error = 0.002506156032137671 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 5 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] = -1.330000000000008 y[1] (closed_form) = 1.155820635649969 y[1] (numeric) = 1.155854126484788 absolute error = 3.3490834818517e-05 relative error = 0.002897580626745223 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 5 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] = -1.320000000000009 y[1] (closed_form) = 1.164121098946692 y[1] (numeric) = 1.164159307940426 absolute error = 3.820899373341291e-05 relative error = 0.003282218127305206 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 5 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] = -1.31000000000001 y[1] (closed_form) = 1.172327455110375 y[1] (numeric) = 1.172370365930433 absolute error = 4.291082005769553e-05 relative error = 0.003660310084067379 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 5 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] = -1.300000000000011 y[1] (closed_form) = 1.180440025302998 y[1] (numeric) = 1.180487621675747 absolute error = 4.759637274864836e-05 relative error = 0.004032087334249041 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 5 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 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; 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 %