##############ECHO OF PROBLEM################# ##############temp/sing4_backpostode.ode################# diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=-1.0 x_end=-2.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=0.1 # 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=2 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=0.0 # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=1.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=1.0 # 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(1.0 / (x * 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 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 min_size 0.5 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 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.9073476791384228e-222 estimated_step_error 1.9073476791384228e-222 Double H and LOOP opt_iter 2 min_size 0.5 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -2.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -1.0 estimated_steps 500000.0 step_error 3.5355339059327375e-21 est_needed_step_err 3.5355339059327375e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.310718689280656e-211 estimated_step_error 1.310718689280656e-211 Double H and LOOP opt_iter 3 min_size 0.5 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -4.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -1.0 estimated_steps 250000.0 step_error 5.0e-21 est_needed_step_err 5.0e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.007181240360502e-201 estimated_step_error 9.007181240360502e-201 Double H and LOOP opt_iter 4 min_size 0.5 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -8.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -1.0 estimated_steps 125000.0 step_error 7.071067811865475e-21 est_needed_step_err 7.071067811865475e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.189675437675637e-190 estimated_step_error 6.189675437675637e-190 Double H and LOOP opt_iter 5 min_size 0.5 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -1.6e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -1.0 estimated_steps 62500.0 step_error 1.0e-20 est_needed_step_err 1.0e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.2534955584111534e-179 estimated_step_error 4.2534955584111534e-179 Double H and LOOP opt_iter 6 min_size 0.5 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -3.2e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -1.0 estimated_steps 31250.0 step_error 1.414213562373095e-20 est_needed_step_err 1.414213562373095e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.922956506983557e-168 estimated_step_error 2.922956506983557e-168 Double H and LOOP opt_iter 7 min_size 0.5 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -6.4e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -1.0 estimated_steps 15625.0 step_error 2.0e-20 est_needed_step_err 2.0e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.008608278830409e-157 estimated_step_error 2.008608278830409e-157 Double H and LOOP opt_iter 8 min_size 0.5 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -0.000128 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -1.0 estimated_steps 7812.5 step_error 2.82842712474619e-20 est_needed_step_err 2.82842712474619e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3802609298318298e-146 estimated_step_error 1.3802609298318298e-146 Double H and LOOP opt_iter 9 min_size 0.5 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -0.000256 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -1.0 estimated_steps 3906.25 step_error 4.0e-20 est_needed_step_err 4.0e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.484473859970062e-136 estimated_step_error 9.484473859970062e-136 Double H and LOOP opt_iter 10 min_size 0.5 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -0.000512 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -1.0 estimated_steps 1953.125 step_error 5.65685424949238e-20 est_needed_step_err 5.65685424949238e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.516846597997249e-125 estimated_step_error 6.516846597997249e-125 Double H and LOOP opt_iter 11 min_size 0.5 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -0.001024 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -1.0 estimated_steps 976.5625 step_error 8.0e-20 est_needed_step_err 8.0e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.4771965728752666e-114 estimated_step_error 4.4771965728752666e-114 Double H and LOOP opt_iter 12 min_size 0.5 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -0.002048 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -1.0 estimated_steps 488.28125 step_error 1.131370849898476e-19 est_needed_step_err 1.131370849898476e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.0751311875037823e-103 estimated_step_error 3.0751311875037823e-103 Double H and LOOP opt_iter 13 min_size 0.5 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -0.004096 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -1.0 estimated_steps 244.140625 step_error 1.6e-19 est_needed_step_err 1.6e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.1110512400032435e-92 estimated_step_error 2.1110512400032435e-92 Double H and LOOP opt_iter 14 min_size 0.5 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -0.008192 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -1.0 estimated_steps 122.0703125 step_error 2.262741699796952e-19 est_needed_step_err 2.262741699796952e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.4477353800920596e-81 estimated_step_error 1.4477353800920596e-81 Double H and LOOP opt_iter 15 min_size 0.5 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -0.016384 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -1.0 estimated_steps 61.03515625 step_error 3.2e-19 est_needed_step_err 3.2e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.908095791012024e-71 estimated_step_error 9.908095791012024e-71 Double H and LOOP opt_iter 16 min_size 0.5 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -0.032768 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -1.0 estimated_steps 30.517578125 step_error 4.525483399593904e-19 est_needed_step_err 4.525483399593904e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.753246192812156e-60 estimated_step_error 6.753246192812156e-60 Double H and LOOP opt_iter 17 min_size 0.5 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -0.065536 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -1.0 estimated_steps 15.2587890625 step_error 6.4e-19 est_needed_step_err 6.4e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.565404193417324e-49 estimated_step_error 4.565404193417324e-49 Double H and LOOP opt_iter 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL START of Soultion TOP MAIN SOLVE Loop x[1] -1.1 y[1] (closed_form) 0.45248868778280543 y[1] (numeric) 0.45248868778280543 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h -0.1 Radius of convergence (given) for eq 1 1.4866068747318506 Order of pole (given) 1.0 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 1.4866068747318473 Order of pole (six term test) 0.999999999999929 TOP MAIN SOLVE Loop x[1] -1.2000000000000002 y[1] (closed_form) 0.40983606557377045 y[1] (numeric) 0.4098360655737705 absolute error 5.551115123125783e-17 relative error 1.3544720900426911e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h -0.1 Radius of convergence (given) for eq 1 1.562049935181331 Order of pole (given) 1.0 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 1.5620499351813342 Order of pole (six term test) 1.0000000000000675 TOP MAIN SOLVE Loop x[1] -1.3000000000000003 y[1] (closed_form) 0.3717472118959107 y[1] (numeric) 0.3717472118959108 absolute error 1.1102230246251565e-16 relative error 2.986499936241672e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h -0.1 Radius of convergence (given) for eq 1 1.6401219466856727 Order of pole (given) 1.0 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 1.640121946685608 Order of pole (six term test) 0.9999999999988667 TOP MAIN SOLVE Loop x[1] -1.4000000000000004 y[1] (closed_form) 0.3378378378378377 y[1] (numeric) 0.3378378378378379 absolute error 1.6653345369377348e-16 relative error 4.929390229335697e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h -0.1 Radius of convergence (given) for eq 1 1.7204650534085255 Order of pole (given) 1.0 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 1.7204650534084829 Order of pole (six term test) 0.9999999999992397 TOP MAIN SOLVE Loop x[1] -1.5000000000000004 y[1] (closed_form) 0.30769230769230754 y[1] (numeric) 0.30769230769230776 absolute error 2.220446049250313e-16 relative error 7.216449660063521e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h -0.1 Radius of convergence (given) for eq 1 1.802775637731995 Order of pole (given) 1.0 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 1.8027756377320114 Order of pole (six term test) 1.000000000000341 TOP MAIN SOLVE Loop x[1] -1.6000000000000005 y[1] (closed_form) 0.28089887640449424 y[1] (numeric) 0.28089887640449446 absolute error 2.220446049250313e-16 relative error 7.904787935331118e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h -0.1 Radius of convergence (given) for eq 1 1.8867962264113212 Order of pole (given) 1.0 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 1.8867962264113054 Order of pole (six term test) 0.9999999999997655 TOP MAIN SOLVE Loop x[1] -1.7000000000000006 y[1] (closed_form) 0.2570694087403598 y[1] (numeric) 0.25706940874036 absolute error 2.220446049250313e-16 relative error 8.637535131583722e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h -0.1 Radius of convergence (given) for eq 1 1.9723082923316024 Order of pole (given) 1.0 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 1.9723082923316682 Order of pole (six term test) 1.000000000000984 TOP MAIN SOLVE Loop x[1] -1.8000000000000007 y[1] (closed_form) 0.23584905660377348 y[1] (numeric) 0.2358490566037737 absolute error 2.220446049250313e-16 relative error 9.414691248821331e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h -0.1 Radius of convergence (given) for eq 1 2.0591260281974004 Order of pole (given) 1.0 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 2.0591260281973836 Order of pole (six term test) 0.9999999999997442 TOP MAIN SOLVE Loop x[1] -1.9000000000000008 y[1] (closed_form) 0.21691973969631223 y[1] (numeric) 0.21691973969631248 absolute error 2.498001805406602e-16 relative error 1.1515788322924444e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h -0.1 Radius of convergence (given) for eq 1 2.1470910553583895 Order of pole (given) 1.0 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 2.147091055358432 Order of pole (six term test) 1.0000000000007567 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; Iterations 10 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Expected Time Remaining 0.0 Seconds Optimized Time Remaining 0.0 Seconds Expected Total Time 0.0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 0.0%