##############ECHO OF PROBLEM################# ##############temp/expt_sin_lin_newpostode.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 ## Comment 1 # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ## Comment 2 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK ## Comment 3 x_start=0.1 x_end=0.11 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=1000000 ## Comment 4 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.001 $glob_look_poles=true $glob_max_iter=10000000 $glob_max_minutes=3 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK ## Comment 5 def exact_soln_y (x) ## Comment 6 return(expt(sin(x),2.0*x+1.0)) ## Comment 7 end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 opt_iter 1 $glob_desired_digits_correct 10 desired_abs_gbl_error 1.0e-10 range 0.009999999999999995 estimated_steps 9.999999999999995 step_error 1.0000000000000006e-11 est_needed_step_err 1.0000000000000006e-11 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 value3 3.7287844517317426e-55 max_value3 3.7287844517317426e-55 value3 3.7287844517317426e-55 best_h 0.001 START of Soultion x[1] 0.1 y[1] (analytic) 0.06296962708006738 y[1] (numeric) 0.06296962708006738 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.1 y[1] (analytic) 0.06296962708006738 y[1] (numeric) 0.06296962708006738 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 NO POLE TOP MAIN SOLVE Loop x[1] 0.101 y[1] (analytic) 0.06343171666528524 y[1] (numeric) 0.06343171666528524 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 NO POLE TOP MAIN SOLVE Loop x[1] 0.10200000000000001 y[1] (analytic) 0.06389216432076887 y[1] (numeric) 0.06389216459537395 absolute error 2.7460507479037943e-10 relative error 4.29794604251833e-07% Correct digits 8 h 0.001 NO POLE TOP MAIN SOLVE Loop x[1] 0.10300000000000001 y[1] (analytic) 0.06435099580421433 y[1] (numeric) 0.06435099635293964 absolute error 5.487253151859051e-10 relative error 8.527067970406904e-07% Correct digits 8 h 0.001 NO POLE TOP MAIN SOLVE Loop x[1] 0.10400000000000001 y[1] (analytic) 0.0648082364607342 y[1] (numeric) 0.06480823728310636 absolute error 8.223721564837305e-10 relative error 1.2689315454247648e-06% Correct digits 7 h 0.001 NO POLE TOP MAIN SOLVE Loop x[1] 0.10500000000000001 y[1] (analytic) 0.06526391123230128 y[1] (numeric) 0.06526391232785818 absolute error 1.0955568952031314e-09 relative error 1.678656510952264e-06% Correct digits 7 h 0.001 NO POLE TOP MAIN SOLVE Loop x[1] 0.10600000000000001 y[1] (analytic) 0.06571804466690874 y[1] (numeric) 0.06571804603519936 absolute error 1.368290619696566e-09 relative error 2.0820622808115087e-06% Correct digits 7 h 0.001 NO POLE TOP MAIN SOLVE Loop x[1] 0.10700000000000001 y[1] (analytic) 0.06617066092745721 y[1] (numeric) 0.06617066256804159 absolute error 1.6405843766831296e-09 relative error 2.479322941147134e-06% Correct digits 7 h 0.001 NO POLE TOP MAIN SOLVE Loop x[1] 0.10800000000000001 y[1] (analytic) 0.06662178380037974 y[1] (numeric) 0.06662178571282872 absolute error 1.9124489769595243e-09 relative error 2.87060608087264e-06% Correct digits 7 h 0.001 NO POLE TOP MAIN SOLVE Loop x[1] 0.10900000000000001 y[1] (analytic) 0.06707143670401347 y[1] (numeric) 0.06707143888790863 absolute error 2.1838951619335134e-09 relative error 3.256073329055186e-06% Correct digits 7 h 0.001 NO POLE 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 10 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 110.00000000000016%