##############ECHO OF PROBLEM################# ##############temp/lin_arcsinpostode.ode################# diff ( y , x , 1 ) = arcsin ( 0.1 * x + 0.2 ) ; ! #BEGIN FIRST INPUT BLOCK max_terms=30 # Digits:=32; ELIMINATED in preodein.rb ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=-0.8 x_end=0.8 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true # 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=0 #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(10.0 * (0.1 * x + 0.2) * arcsin(0.1 * x + 0.2 ) + 10.0 * sqrt(1.0 - expt((0.1 * x + 0.2) , 2 ))) 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 1.6 estimated_steps 1600000.0000000002 step_error 2.6352313834736493e-21 est_needed_step_err 2.6352313834736493e-21 opt_iter 1 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 min_size 10.072086775666431 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 10.072086775666431 desired_abs_gbl_error 1.007208677566643e-15 range 1.6 estimated_steps 1600000.0000000002 step_error 2.6542279168306096e-20 est_needed_step_err 2.6542279168306096e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 2 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 min_size 10.072086775666431 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 10.072086775666431 desired_abs_gbl_error 1.007208677566643e-15 range 1.6 estimated_steps 800000.0000000001 step_error 3.753645117611135e-20 est_needed_step_err 3.753645117611135e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 3 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 min_size 10.072086775666431 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 10.072086775666431 desired_abs_gbl_error 1.007208677566643e-15 range 1.6 estimated_steps 400000.00000000006 step_error 5.308455833661219e-20 est_needed_step_err 5.308455833661219e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 4 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 min_size 10.072086775666431 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 10.072086775666431 desired_abs_gbl_error 1.007208677566643e-15 range 1.6 estimated_steps 200000.00000000003 step_error 7.50729023522227e-20 est_needed_step_err 7.50729023522227e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 5 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 min_size 10.072086775666431 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 10.072086775666431 desired_abs_gbl_error 1.007208677566643e-15 range 1.6 estimated_steps 100000.00000000001 step_error 1.0616911667322438e-19 est_needed_step_err 1.0616911667322438e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 6 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 min_size 10.072086775666431 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 10.072086775666431 desired_abs_gbl_error 1.007208677566643e-15 range 1.6 estimated_steps 50000.00000000001 step_error 1.501458047044454e-19 est_needed_step_err 1.501458047044454e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 7 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 min_size 10.072086775666431 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 10.072086775666431 desired_abs_gbl_error 1.007208677566643e-15 range 1.6 estimated_steps 25000.000000000004 step_error 2.1233823334644877e-19 est_needed_step_err 2.1233823334644877e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 8 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 min_size 10.072086775666431 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 10.072086775666431 desired_abs_gbl_error 1.007208677566643e-15 range 1.6 estimated_steps 12500.000000000002 step_error 3.002916094088908e-19 est_needed_step_err 3.002916094088908e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 9 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 min_size 10.072086775666431 $glob_desired_digits_correct 16 estimated_h 0.000256 estimated_answer 10.072086775666431 desired_abs_gbl_error 1.007208677566643e-15 range 1.6 estimated_steps 6250.000000000001 step_error 4.2467646669289754e-19 est_needed_step_err 4.2467646669289754e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 10 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 min_size 10.072086775666431 $glob_desired_digits_correct 16 estimated_h 0.000512 estimated_answer 10.072086775666431 desired_abs_gbl_error 1.007208677566643e-15 range 1.6 estimated_steps 3125.0000000000005 step_error 6.005832188177816e-19 est_needed_step_err 6.005832188177816e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 11 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 min_size 10.072086775666431 $glob_desired_digits_correct 16 estimated_h 0.001024 estimated_answer 10.072086775666431 desired_abs_gbl_error 1.007208677566643e-15 range 1.6 estimated_steps 1562.5000000000002 step_error 8.493529333857951e-19 est_needed_step_err 8.493529333857951e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 12 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 min_size 10.072086775666431 $glob_desired_digits_correct 16 estimated_h 0.002048 estimated_answer 10.072086775666431 desired_abs_gbl_error 1.007208677566643e-15 range 1.6 estimated_steps 781.2500000000001 step_error 1.2011664376355632e-18 est_needed_step_err 1.2011664376355632e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 13 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 min_size 10.072086775666431 $glob_desired_digits_correct 16 estimated_h 0.004096 estimated_answer 10.072086775666431 desired_abs_gbl_error 1.007208677566643e-15 range 1.6 estimated_steps 390.62500000000006 step_error 1.6987058667715902e-18 est_needed_step_err 1.6987058667715902e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 14 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 min_size 10.072086775666431 $glob_desired_digits_correct 16 estimated_h 0.008192 estimated_answer 10.072086775666431 desired_abs_gbl_error 1.007208677566643e-15 range 1.6 estimated_steps 195.31250000000003 step_error 2.4023328752711265e-18 est_needed_step_err 2.4023328752711265e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 15 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 min_size 10.072086775666431 $glob_desired_digits_correct 16 estimated_h 0.016384 estimated_answer 10.072086775666431 desired_abs_gbl_error 1.007208677566643e-15 range 1.6 estimated_steps 97.65625000000001 step_error 3.3974117335431803e-18 est_needed_step_err 3.3974117335431803e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 16 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 min_size 10.072086775666431 $glob_desired_digits_correct 16 estimated_h 0.032768 estimated_answer 10.072086775666431 desired_abs_gbl_error 1.007208677566643e-15 range 1.6 estimated_steps 48.82812500000001 step_error 4.804665750542253e-18 est_needed_step_err 4.804665750542253e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 17 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 min_size 10.072086775666431 $glob_desired_digits_correct 16 estimated_h 0.065536 estimated_answer 10.072086775666431 desired_abs_gbl_error 1.007208677566643e-15 range 1.6 estimated_steps 24.414062500000004 step_error 6.794823467086361e-18 est_needed_step_err 6.794823467086361e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL 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 START of Soultion TOP MAIN SOLVE Loop x[1] -0.8 y[1] (closed_form) 10.072086775666431 y[1] (numeric) 10.072086775666431 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -0.7000000000000001 y[1] (closed_form) 10.084619612112183 y[1] (numeric) 10.084619403258426 absolute error 2.0885375739965184e-07 relative error 2.0710127444847496e-06% Desired digits 16 Estimated correct digits 14 Correct digits 8 h 0.1 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 TOP MAIN SOLVE Loop x[1] -0.6000000000000001 y[1] (closed_form) 10.098161016183049 y[1] (numeric) 10.098160580546129 absolute error 4.356369203151189e-07 relative error 4.314022321658157e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.1 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 TOP MAIN SOLVE Loop x[1] -0.5000000000000001 y[1] (closed_form) 10.112712375807623 y[1] (numeric) 10.112711695244144 absolute error 6.805634793494164e-07 relative error 6.729781823692628e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.1 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 TOP MAIN SOLVE Loop x[1] -0.40000000000000013 y[1] (closed_form) 10.12827518812551 y[1] (numeric) 10.128274244259236 absolute error 9.438662740279824e-07 relative error 9.3191215334925e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.1 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 TOP MAIN SOLVE Loop x[1] -0.30000000000000016 y[1] (closed_form) 10.144851060913583 y[1] (numeric) 10.144849835115973 absolute error 1.225797609194501e-06 relative error 1.2082953232475681e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 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 TOP MAIN SOLVE Loop x[1] -0.20000000000000015 y[1] (closed_form) 10.162441714130136 y[1] (numeric) 10.162440187500174 absolute error 1.526629962000925e-06 relative error 1.5022275206540738e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 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 TOP MAIN SOLVE Loop x[1] -0.10000000000000014 y[1] (closed_form) 10.181048981581155 y[1] (numeric) 10.18104713492443 absolute error 1.8466567244246335e-06 relative error 1.8138177389829637e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 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 TOP MAIN SOLVE Loop x[1] -1.3877787807814457e-16 y[1] (closed_form) 10.200674812713373 y[1] (numeric) 10.20067262652033 absolute error 2.1861930434852184e-06 relative error 2.1431847241718828e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 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 TOP MAIN SOLVE Loop x[1] 0.09999999999999987 y[1] (closed_form) 10.221321274539148 y[1] (numeric) 10.221318728962443 absolute error 2.5455767058701895e-06 relative error 2.490457581263106e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 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 TOP MAIN SOLVE Loop x[1] 0.19999999999999987 y[1] (closed_form) 10.242990553698707 y[1] (numeric) 10.242987628529582 absolute error 2.9251691255893775e-06 relative error 2.8557764553762176e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 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 TOP MAIN SOLVE Loop x[1] 0.2999999999999999 y[1] (closed_form) 10.265684958665728 y[1] (numeric) 10.265681633309326 absolute error 3.3253564026836102e-06 relative error 3.2392932532733986e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 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 TOP MAIN SOLVE Loop x[1] 0.3999999999999999 y[1] (closed_form) 10.289406922102788 y[1] (numeric) 10.28940317555231 absolute error 3.7465504778566583e-06 relative error 3.641172427352107e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 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 TOP MAIN SOLVE Loop x[1] 0.4999999999999999 y[1] (closed_form) 10.314159003373739 y[1] (numeric) 10.31415481418335 absolute error 4.1891903883595205e-06 relative error 4.0615918243932886e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 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 TOP MAIN SOLVE Loop x[1] 0.5999999999999999 y[1] (closed_form) 10.339943891220669 y[1] (numeric) 10.339939237477052 absolute error 4.653743616245265e-06 relative error 4.5007435873966557e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 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 TOP MAIN SOLVE Loop x[1] 0.6999999999999998 y[1] (closed_form) 10.3667644066138 y[1] (numeric) 10.366759265906234 absolute error 5.14070756629792e-06 relative error 4.958835143411039e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 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 TOP MAIN SOLVE Loop x[1] 0.7999999999999998 y[1] (closed_form) 10.394623505783319 y[1] (numeric) 10.394617855172152 absolute error 5.650611166529984e-06 relative error 5.436090266651909e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 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 ) = arcsin ( 0.1 * x + 0.2 ) ; Iterations 17 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 112.49999999999997%