##############ECHO OF PROBLEM################# ##############temp/sqrtpostode.ode################# diff ( y , x , 1 ) = sqrt ( x ) ; ! /* 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(0.2); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=c(0.001); glob_max_h=c(0.01); glob_type_given_pole=1; array_given_rad_poles[1][1]=c(0.0); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(1.5); 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=false; 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(2.0)*expt(c(x),c(1.5))/c(3.0)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.0210818510677892 y[1] (numeric) = 0.0210818510677892 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = 0.02432191512927294 y[1] (numeric) = 0.02432191512927294 absolute error = 3.469446951953614e-18 relative error = 1.426469475579215e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 0.02771281292110205 y[1] (numeric) = 0.02771281292110205 absolute error = 3.469446951953614e-18 relative error = 1.251928832280966e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 0.03124811105402125 y[1] (numeric) = 0.03124811105402125 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 0.03492213560989014 y[1] (numeric) = 0.03492213560989012 absolute error = 1.387778780781446e-17 relative error = 3.973923004835991e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 0.03872983346207419 y[1] (numeric) = 0.03872983346207417 absolute error = 2.081668171172169e-17 relative error = 5.37484410618657e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 0.04266666666666669 y[1] (numeric) = 0.04266666666666666 absolute error = 2.775557561562891e-17 relative error = 6.505213034913024e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 0.04672853042366685 y[1] (numeric) = 0.04672853042366681 absolute error = 4.163336342344337e-17 relative error = 8.909623959061443e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 0.05091168824543146 y[1] (numeric) = 0.05091168824543141 absolute error = 4.163336342344337e-17 relative error = 8.17756488897799e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = 0.05521271995151524 y[1] (numeric) = 0.0552127199515152 absolute error = 4.163336342344337e-17 relative error = 7.54053838680715e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 Finished! diff ( y , x , 1 ) = sqrt ( 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 %