##############ECHO OF PROBLEM################# ##############temp/expt_sin_lin_new_sm_hpostode.ode################# diff ( y , x , 1 ) = ( expt ( sin ( x ) , ( 2.0 * x + 1.0 ) ) ) * ( ( 2.0 * ln ( sin ( x ) ) ) + ( ( ( 2.0 * x + 1.0 ) * cos ( x ) ) / sin ( x ) ) ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.1; x_end=0.11; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=0; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(expt(sin(x),2.0*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 = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.009999999999999995 estimated_steps = 9999.999999999996 step_error = 1e-12 est_needed_step_err = 1e-12 opt_iter = 1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.005263 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.06296962708006738 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.009999999999999995 estimated_steps = 9999.999999999996 step_error = 1e-12 est_needed_step_err = 1e-12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.776969463336468e-133 estimated_step_error = 3.776969463336468e-133 Double H and LOOP opt_iter = 2 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.00507 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.06296962708006738 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.009999999999999995 estimated_steps = 4999.999999999998 step_error = 1.414213562373095e-12 est_needed_step_err = 1.414213562373095e-12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.539797489598402e-125 estimated_step_error = 1.539797489598402e-125 Double H and LOOP opt_iter = 3 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.00507 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.06296962708006738 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.009999999999999995 estimated_steps = 2499.999999999999 step_error = 2e-12 est_needed_step_err = 2e-12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.033330654597698e-117 estimated_step_error = 1.033330654597698e-117 Double H and LOOP opt_iter = 4 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.00507 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.06296962708006738 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.009999999999999995 estimated_steps = 1250 step_error = 2.828427124746191e-12 est_needed_step_err = 2.828427124746191e-12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.934431113027482e-110 estimated_step_error = 6.934431113027482e-110 Double H and LOOP opt_iter = 5 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.00507 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.06296962708006738 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.009999999999999995 estimated_steps = 624.9999999999998 step_error = 4.000000000000001e-12 est_needed_step_err = 4.000000000000001e-12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.653438742818478e-102 estimated_step_error = 4.653438742818478e-102 Double H and LOOP opt_iter = 6 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.00507 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.06296962708006738 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.009999999999999995 estimated_steps = 312.4999999999999 step_error = 5.656854249492381e-12 est_needed_step_err = 5.656854249492381e-12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.122629384214915e-94 estimated_step_error = 3.122629384214915e-94 Double H and LOOP opt_iter = 7 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.00507 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.06296962708006738 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.009999999999999995 estimated_steps = 156.2499999999999 step_error = 8.000000000000001e-12 est_needed_step_err = 8.000000000000001e-12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.095238397065232e-86 estimated_step_error = 2.095238397065232e-86 Double H and LOOP opt_iter = 8 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.00507 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.06296962708006738 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.009999999999999995 estimated_steps = 78.12499999999997 step_error = 1.131370849898476e-11 est_needed_step_err = 1.131370849898476e-11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.405657753171161e-78 estimated_step_error = 1.405657753171161e-78 Double H and LOOP opt_iter = 9 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.00507 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.06296962708006738 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.009999999999999995 estimated_steps = 39.06249999999999 step_error = 1.6e-11 est_needed_step_err = 1.6e-11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.42740413929637e-71 estimated_step_error = 9.42740413929637e-71 Double H and LOOP opt_iter = 10 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.00507 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.06296962708006738 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.009999999999999995 estimated_steps = 19.53124999999999 step_error = 2.262741699796953e-11 est_needed_step_err = 2.262741699796953e-11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.318846388462385e-63 estimated_step_error = 6.318846388462385e-63 Double H and LOOP opt_iter = 11 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.00507 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.06296962708006738 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.009999999999999995 estimated_steps = 9.765624999999996 step_error = 3.200000000000001e-11 est_needed_step_err = 3.200000000000001e-11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.23010578733596e-55 estimated_step_error = 4.23010578733596e-55 Double H and LOOP opt_iter = 12 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.00507 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.06296962708006738 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.009999999999999995 estimated_steps = 4.882812499999998 step_error = 4.525483399593905e-11 est_needed_step_err = 4.525483399593905e-11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.824919293729804e-47 estimated_step_error = 2.824919293729804e-47 Double H and LOOP opt_iter = 13 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.00507 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.06296962708006738 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.009999999999999995 estimated_steps = 2.441406249999999 step_error = 6.400000000000001e-11 est_needed_step_err = 6.400000000000001e-11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.877443005203316e-39 estimated_step_error = 1.877443005203316e-39 Double H and LOOP opt_iter = 14 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.00507 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.06296962708006738 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.009999999999999995 estimated_steps = 1.220703125 step_error = 9.05096679918781e-11 est_needed_step_err = 9.05096679918781e-11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.236029294846083e-31 estimated_step_error = 1.236029294846083e-31 Double H and LOOP opt_iter = 15 SETTING H FOR DISPLAY INTERVAL SETTING H FOR POLE NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06104 Order of pole (three term test) = 0.00507 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.06296962708006738 y[1] (numeric) = 0.06296962708006738 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.006103504702241071 NO INFO (given) for Equation 1 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 ) = ( expt ( sin ( x ) , ( 2.0 * x + 1.0 ) ) ) * ( ( 2.0 * ln ( sin ( x ) ) ) + ( ( ( 2.0 * x + 1.0 ) * cos ( x ) ) / sin ( x ) ) ) ; Iterations = 2 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 183.1 %