##############ECHO OF PROBLEM################# ##############temp/sin_sqrt_linpostode.ode################# diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=2.0 x_end=3.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=0.0001 $glob_upper_ratio_limit=1.001 $glob_lower_ratio_limit=0.999 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=-1.5 # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=0.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=0.5 # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=0.0 # ELIMINATED in preodein.rb #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 def exact_soln_y (x) return(sin(sqrt(2.0*x+3.0))-sqrt(2.0*x+3.0)*cos(sqrt(2.0*x+3.0))) 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 16 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 1.0 estimated_steps 1000000.0 step_error 2.5e-21 est_needed_step_err 2.5e-21 opt_iter 1 Radius of convergence (given) for eq 1 3.5 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 3.99973439318416 Order of pole (six term test) -1.3130478986159808 min_size 2.80289196959102 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 2.80289196959102 desired_abs_gbl_error 2.80289196959102e-16 range 1.0 estimated_steps 1000000.0 step_error 7.00722992397755e-21 est_needed_step_err 7.00722992397755e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.791154658409449e-240 estimated_step_error 1.791154658409449e-240 Double H and LOOP opt_iter 2 Radius of convergence (given) for eq 1 3.5 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 3.99973439318416 Order of pole (six term test) -1.3130478986159808 min_size 2.80289196959102 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 2.80289196959102 desired_abs_gbl_error 2.80289196959102e-16 range 1.0 estimated_steps 500000.0 step_error 9.909719593155644e-21 est_needed_step_err 9.909719593155644e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.230871943468012e-229 estimated_step_error 1.230871943468012e-229 Double H and LOOP opt_iter 3 Radius of convergence (given) for eq 1 3.5 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 3.99973439318416 Order of pole (six term test) -1.3130478986159808 min_size 2.80289196959102 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 2.80289196959102 desired_abs_gbl_error 2.80289196959102e-16 range 1.0 estimated_steps 250000.0 step_error 1.40144598479551e-20 est_needed_step_err 1.40144598479551e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.45848531622724e-219 estimated_step_error 8.45848531622724e-219 Double H and LOOP opt_iter 4 Radius of convergence (given) for eq 1 3.5 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 3.99973439318416 Order of pole (six term test) -1.3130478986159808 min_size 2.80289196959102 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 2.80289196959102 desired_abs_gbl_error 2.80289196959102e-16 range 1.0 estimated_steps 125000.0 step_error 1.9819439186311287e-20 est_needed_step_err 1.9819439186311287e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.812623726234864e-208 estimated_step_error 5.812623726234864e-208 Double H and LOOP opt_iter 5 Radius of convergence (given) for eq 1 3.5 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 3.99973439318416 Order of pole (six term test) -1.3130478986159808 min_size 2.80289196959102 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 2.80289196959102 desired_abs_gbl_error 2.80289196959102e-16 range 1.0 estimated_steps 62500.0 step_error 2.80289196959102e-20 est_needed_step_err 2.80289196959102e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.9944003172711626e-197 estimated_step_error 3.9944003172711626e-197 Double H and LOOP opt_iter 6 Radius of convergence (given) for eq 1 3.5 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 3.99973439318416 Order of pole (six term test) -1.3130478986159808 min_size 2.80289196959102 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 2.80289196959102 desired_abs_gbl_error 2.80289196959102e-16 range 1.0 estimated_steps 31250.0 step_error 3.9638878372622574e-20 est_needed_step_err 3.9638878372622574e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.744925097867764e-186 estimated_step_error 2.744925097867764e-186 Double H and LOOP opt_iter 7 Radius of convergence (given) for eq 1 3.5 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 3.99973439318416 Order of pole (six term test) -1.3130478986159808 min_size 2.80289196959102 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 2.80289196959102 desired_abs_gbl_error 2.80289196959102e-16 range 1.0 estimated_steps 15625.0 step_error 5.60578393918204e-20 est_needed_step_err 5.60578393918204e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.8862900567128852e-175 estimated_step_error 1.8862900567128852e-175 Double H and LOOP opt_iter 8 SETTING H FOR MAX H Radius of convergence (given) for eq 1 3.5 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 3.1247924946751255 Order of pole (six term test) -1.3130478986159808 START of Soultion TOP MAIN SOLVE Loop x[1] 2.0 y[1] (closed_form) 2.80289196959102 y[1] (numeric) 2.80289196959102 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.0001 Radius of convergence (given) for eq 1 3.5 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 3.9997343936297693 Order of pole (six term test) -1.313047889560556 TOP MAIN SOLVE Loop x[1] 2.100000000000211 y[1] (closed_form) 2.848803743596383 y[1] (numeric) 2.848805410488842 absolute error 1.666892459173397e-06 relative error 5.8512014487494346e-05% Desired digits 16 Estimated correct digits 12 Correct digits 7 h 0.0001 Radius of convergence (given) for eq 1 3.600000000000211 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 4.070150993696462 Order of pole (six term test) -1.3302989574309532 TOP MAIN SOLVE Loop x[1] 2.200000000000422 y[1] (closed_form) 2.891373776647514 y[1] (numeric) 2.8913771179620866 absolute error 3.341314572580245e-06 relative error 0.00011556148843732089% Desired digits 16 Estimated correct digits 12 Correct digits 6 h 0.0001 Radius of convergence (given) for eq 1 3.700000000000422 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 4.138736048344006 Order of pole (six term test) -1.3470355286042128 TOP MAIN SOLVE Loop x[1] 2.300000000000633 y[1] (closed_form) 2.93058958868788 y[1] (numeric) 2.9305946094031707 absolute error 5.020715290626754e-06 relative error 0.00017132099663517506% Desired digits 16 Estimated correct digits 12 Correct digits 6 h 0.0001 Radius of convergence (given) for eq 1 3.800000000000633 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 4.205683816887706 Order of pole (six term test) -1.3632125733348737 TOP MAIN SOLVE Loop x[1] 2.400000000000844 y[1] (closed_form) 2.9664436394574647 y[1] (numeric) 2.9664503421613055 absolute error 6.702703840844038e-06 relative error 0.00022595082379754569% Desired digits 16 Estimated correct digits 12 Correct digits 6 h 0.0001 Radius of convergence (given) for eq 1 3.900000000000844 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 4.271215288007452 Order of pole (six term test) -1.3787868683610665 TOP MAIN SOLVE Loop x[1] 2.500000000001055 y[1] (closed_form) 2.9989330194379025 y[1] (numeric) 2.9989414044763336 absolute error 8.385038431146796e-06 relative error 0.00027960072388407076% Desired digits 16 Estimated correct digits 12 Correct digits 6 h 0.0001 Radius of convergence (given) for eq 1 4.000000000001055 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 4.335583366129958 Order of pole (six term test) -1.3937167023825552 TOP MAIN SOLVE Loop x[1] 2.600000000001266 y[1] (closed_form) 3.0280591621941597 y[1] (numeric) 3.0280692278102657 absolute error 1.0065616105947583e-05 relative error 0.00033241147437337203% Desired digits 16 Estimated correct digits 12 Correct digits 6 h 0.0001 Radius of convergence (given) for eq 1 4.100000000001266 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 4.399079726429524 Order of pole (six term test) -1.4079618148005135 TOP MAIN SOLVE Loop x[1] 2.700000000001477 y[1] (closed_form) 3.0538275761017757 y[1] (numeric) 3.0538393185652772 absolute error 1.1742463501551725e-05 relative error 0.00038451625735009675% Desired digits 16 Estimated correct digits 12 Correct digits 6 h 0.0001 Radius of convergence (given) for eq 1 4.200000000001477 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 4.462042254384042 Order of pole (six term test) -1.421483214377714 TOP MAIN SOLVE Loop x[1] 2.8000000000016882 y[1] (closed_form) 3.0762475936905456 y[1] (numeric) 3.076261007419004 absolute error 1.3413728458644414e-05 relative error 0.00043604190007840327% Desired digits 16 Estimated correct digits 12 Correct digits 6 h 0.0001 Radius of convergence (given) for eq 1 4.300000000001688 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 4.524855643033655 Order of pole (six term test) -1.4342443330701524 TOP MAIN SOLVE Loop x[1] 2.9000000000018993 y[1] (closed_form) 3.0953321370426665 y[1] (numeric) 3.095347214714997 absolute error 1.5077672330665592e-05 relative error 0.00048710999864043863% Desired digits 16 Estimated correct digits 12 Correct digits 6 h 0.0001 Radius of convergence (given) for eq 1 4.400000000001899 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 4.58791168317893 Order of pole (six term test) -1.4462173327694199 Finished! diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations 10000 Total Elapsed Time 8 Seconds Elapsed Time(since restart) 8 Seconds Time to Timeout 2 Minutes 52.0 Seconds Percent Done 100.01000000021105%