##############ECHO OF PROBLEM################# ##############temp/ln_sqrtpostode.ode################# diff ( y , x , 1 ) = ln ( sqrt ( 0.1 * x + 0.2 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=10.0; x_end=11.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=0.001; glob_type_given_pole=1; array_given_rad_poles[1][1]=-2.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=0.5; array_given_ord_poles[1][2]=0.0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=16; glob_max_minutes=3.0; glob_subiter_method=3; glob_max_iter=100000000; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(5.0 * ln(0.1 * x + 0.2) * ( 0.1 * x + 0.2) - 0.5 * x - 1.0); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.001 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 1000 step_error = 7.905694150420949e-20 est_needed_step_err = 7.905694150420949e-20 opt_iter = 1 Radius of convergence (given) for eq 1 = 12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.01 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 min_size = 4.906070659236272 glob_desired_digits_correct = 16 estimated_h = 0.001 estimated_answer = 4.906070659236272 desired_abs_gbl_error = 4.906070659236273e-16 range = 1 estimated_steps = 1000 step_error = 3.878589411227605e-19 est_needed_step_err = 3.878589411227605e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.070348865094756e-150 estimated_step_error = 6.070348865094756e-150 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.01 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 min_size = 4.906070659236272 glob_desired_digits_correct = 16 estimated_h = 0.002 estimated_answer = 4.906070659236272 desired_abs_gbl_error = 4.906070659236273e-16 range = 1 estimated_steps = 500 step_error = 5.485153748234755e-19 est_needed_step_err = 5.485153748234755e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.171347320877985e-139 estimated_step_error = 4.171347320877985e-139 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.01 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 min_size = 4.906070659236272 glob_desired_digits_correct = 16 estimated_h = 0.004 estimated_answer = 4.906070659236272 desired_abs_gbl_error = 4.906070659236273e-16 range = 1 estimated_steps = 250 step_error = 7.75717882245521e-19 est_needed_step_err = 7.75717882245521e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.866301778109234e-128 estimated_step_error = 2.866301778109234e-128 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.01 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 min_size = 4.906070659236272 glob_desired_digits_correct = 16 estimated_h = 0.008 estimated_answer = 4.906070659236272 desired_abs_gbl_error = 4.906070659236273e-16 range = 1 estimated_steps = 125 step_error = 1.097030749646951e-18 est_needed_step_err = 1.097030749646951e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.969396669208636e-117 estimated_step_error = 1.969396669208636e-117 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.01 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 min_size = 4.906070659236272 glob_desired_digits_correct = 16 estimated_h = 0.016 estimated_answer = 4.906070659236272 desired_abs_gbl_error = 4.906070659236273e-16 range = 1 estimated_steps = 62.5 step_error = 1.551435764491042e-18 est_needed_step_err = 1.551435764491042e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.352931971042742e-106 estimated_step_error = 1.352931971042742e-106 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.01 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 min_size = 4.906070659236272 glob_desired_digits_correct = 16 estimated_h = 0.032 estimated_answer = 4.906070659236272 desired_abs_gbl_error = 4.906070659236273e-16 range = 1 estimated_steps = 31.25 step_error = 2.194061499293902e-18 est_needed_step_err = 2.194061499293902e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.29141305084783e-96 estimated_step_error = 9.29141305084783e-96 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.01 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 min_size = 4.906070659236272 glob_desired_digits_correct = 16 estimated_h = 0.064 estimated_answer = 4.906070659236272 desired_abs_gbl_error = 4.906070659236273e-16 range = 1 estimated_steps = 15.625 step_error = 3.102871528982084e-18 est_needed_step_err = 3.102871528982084e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.376965358027269e-85 estimated_step_error = 6.376965358027269e-85 Double H and LOOP opt_iter = 8 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.385 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 10 y[1] (closed_form) = -4.906070659236272 y[1] (numeric) = -4.906070659236272 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.01 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.1 y[1] (closed_form) = -4.89674682436767 y[1] (numeric) = -4.896746535916293 absolute error = 2.884513765621932e-07 relative error = 5.890673684144202e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 Radius of convergence (given) for eq 1 = 12.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.11 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.2 y[1] (closed_form) = -4.887009761654492 y[1] (numeric) = -4.88700918949254 absolute error = 5.721619524834409e-07 relative error = 1.170781276053224e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 12.2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.21 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.3 y[1] (closed_form) = -4.876862858286394 y[1] (numeric) = -4.876862007038744 absolute error = 8.512476501465471e-07 relative error = 1.745482034009162e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 12.3 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.31 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.4 y[1] (closed_form) = -4.866309446374938 y[1] (numeric) = -4.866308320554294 absolute error = 1.125820643821385e-06 relative error = 2.313499904244772e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 12.4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.41 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.5 y[1] (closed_form) = -4.85535280428619 y[1] (numeric) = -4.855351408296682 absolute error = 1.395989507102513e-06 relative error = 2.875155654744938e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 12.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.51 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.6 y[1] (closed_form) = -4.843996157930665 y[1] (numeric) = -4.843994496071306 absolute error = 1.661859358570439e-06 relative error = 3.43076109969579e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 12.6 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.61 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.7 y[1] (closed_form) = -4.832242682012326 y[1] (numeric) = -4.832240758480326 absolute error = 1.923531999459271e-06 relative error = 3.980619612958349e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 12.7 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.71 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.8 y[1] (closed_form) = -4.820095501238235 y[1] (numeric) = -4.820093320132193 absolute error = 2.181106042442593e-06 relative error = 4.525026613855033e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 12.8 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.81 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.9 y[1] (closed_form) = -4.807557691490405 y[1] (numeric) = -4.807555256813372 absolute error = 2.434677033313903e-06 relative error = 5.064270029714655e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 12.9 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.91 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11 y[1] (closed_form) = -4.794632280961309 y[1] (numeric) = -4.794629596623739 absolute error = 2.684337570002526e-06 relative error = 5.598630745180576e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 13 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.01 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = ln ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 11 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 120 %