##############ECHO OF PROBLEM################# ##############temp/expt_sin_sin_newpostode.ode################# diff ( y , x , 1 ) = expt ( sin ( 2.0 * x + 3.0 ) , sin ( x + 1.0 ) ) * ( ( cos ( x + 1.0 ) * ln ( sin ( 2.0 * x + 3.0 ) ) ) + ( ( 2.0 * sin ( x + 1.0 ) * cos ( 2.0 * x + 3.0 ) ) / sin ( 2.0 * x + 3.0 ) ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=1.8 x_end=1.81 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=1000000 $glob_max_h=0.00001 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.01 $glob_look_poles=true $glob_max_iter=1000000000 $glob_max_minutes=10.0 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(expt(sin(2.0*x+3.0),sin(x+1.0))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 10 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-10 range 0.010000000000000009 estimated_steps 10000.00000000001 step_error 9.99999999999999e-15 est_needed_step_err 9.99999999999999e-15 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1473410958433689e-137 estimated_step_error 1.1473410958433689e-137 best_h 2.0e-06 opt_iter 2 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.69965235308513e-130 estimated_step_error 7.69965235308513e-130 best_h 4.0e-06 opt_iter 3 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.167117815186807e-122 estimated_step_error 5.167117815186807e-122 best_h 8.0e-06 opt_iter 4 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.467551909063044e-114 estimated_step_error 3.467551909063044e-114 best_h 1.6e-05 opt_iter 5 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.3269781130032004e-106 estimated_step_error 2.3269781130032004e-106 best_h 1.0e-05 START of Soultion TOP MAIN SOLVE Loop x[1] 1.8 y[1] (analytic) 0.6766027626496453 y[1] (numeric) 0.6766027626496453 absolute error 0.0 relative error 0.0% Correct digits 16 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.15840744901295245 Order of pole (three term test) 5.610691369629913e-05 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = expt ( sin ( 2.0 * x + 3.0 ) , sin ( x + 1.0 ) ) * ( ( cos ( x + 1.0 ) * ln ( sin ( 2.0 * x + 3.0 ) ) ) + ( ( 2.0 * sin ( x + 1.0 ) * cos ( 2.0 * x + 3.0 ) ) / sin ( 2.0 * x + 3.0 ) ) ) ; Iterations 1000 Total Elapsed Time 3 Seconds Elapsed Time(since restart) 3 Seconds Time to Timeout 9 Minutes 57.0 Seconds Percent Done 100.10000000065568%