##############ECHO OF PROBLEM################# ##############temp/mult_sin_sinpostode.ode################# diff ( y , x , 1 ) = sin ( x ) * sin ( x ) ; ! // 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(0.2); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; // 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(((sin(c(x))) * cos(c(x)))/c(-2.0) + c(x)/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) = 0.0003326673012346917 y[1] (numeric) = 0.0003326673012346917 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09735 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = 0.0004425942297826696 y[1] (numeric) = 0.0004425942297826656 absolute error = 4.011548038196366e-18 relative error = 9.063715178045107e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1065 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 0.0005743433932163533 y[1] (numeric) = 0.0005743433932163488 absolute error = 4.553649124439119e-18 relative error = 7.928443468181018e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1154 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 0.0007298620269612227 y[1] (numeric) = 0.0007298620269612214 absolute error = 1.301042606982605e-18 relative error = 1.782587062926798e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1242 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 0.0009110878589715654 y[1] (numeric) = 0.0009110878589715626 absolute error = 2.818925648462312e-18 relative error = 3.094021746315784e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1328 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 0.001119948334665111 y[1] (numeric) = 0.001119948334665102 absolute error = 8.456776945386935e-18 relative error = 7.551042029019757e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1412 Order of pole (three term test) = 22.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 0.001358359845970561 y[1] (numeric) = 0.001358359845970555 absolute error = 6.288372600415926e-18 relative error = 4.629386402336433e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1493 Order of pole (three term test) = 22.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 0.001628226964796406 y[1] (numeric) = 0.001628226964796397 absolute error = 8.456776945386935e-18 relative error = 5.193856340810799e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1572 Order of pole (three term test) = 22.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 0.001931441681227497 y[1] (numeric) = 0.001931441681227503 absolute error = 5.637851296924623e-18 relative error = 2.918986036037897e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1648 Order of pole (three term test) = 22.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = 0.002269882646754331 y[1] (numeric) = 0.002269882646754329 absolute error = 2.168404344971009e-18 relative error = 9.552935910900835e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1722 Order of pole (three term test) = 22.86 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin ( x ) * sin ( x ) ; Iterations = 100 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 101 %