##############ECHO OF PROBLEM################# ##############temp/sqrt_tonepostode.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(0.5); x_end=c(0.6); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=c(0.01); glob_min_h=c(0.001); 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] = 0.5 y[1] (closed_form) = 0.2357022603955159 y[1] (numeric) = 0.2357022603955159 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] = 0.51 y[1] (closed_form) = 0.2428085665704569 y[1] (numeric) = 0.242808566570457 absolute error = 5.551115123125783e-17 relative error = 2.286210573841096e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (closed_form) = 0.2499848884321699 y[1] (numeric) = 0.24998488843217 absolute error = 8.326672684688674e-17 relative error = 3.330870412572161e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (closed_form) = 0.257230549421245 y[1] (numeric) = 0.2572305494212451 absolute error = 5.551115123125783e-17 relative error = 2.158031048650907e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (closed_form) = 0.2645448922205832 y[1] (numeric) = 0.2645448922205834 absolute error = 1.110223024625157e-16 relative error = 4.196728257748513e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (closed_form) = 0.2719272778601743 y[1] (numeric) = 0.2719272778601745 absolute error = 1.665334536937735e-16 relative error = 6.124190813229314e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000001 y[1] (closed_form) = 0.279377084879121 y[1] (numeric) = 0.2793770848791211 absolute error = 1.110223024625157e-16 relative error = 3.973923004835992e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000001 y[1] (closed_form) = 0.2868937085402886 y[1] (numeric) = 0.2868937085402887 absolute error = 1.110223024625157e-16 relative error = 3.869806104406948e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000001 y[1] (closed_form) = 0.2944765600934045 y[1] (numeric) = 0.2944765600934046 absolute error = 1.110223024625157e-16 relative error = 3.77015754419641e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000001 y[1] (closed_form) = 0.302125066082832 y[1] (numeric) = 0.302125066082832 absolute error = 0 relative error = 0 % 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 %