##############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 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb x_start=c(0.1) x_end=c(0.2) $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=8 $glob_max_minutes=(3.0) $glob_subiter_method=3 $glob_max_iter=100000 $glob_upper_ratio_limit=c(1.000001) $glob_lower_ratio_limit=c(0.999999) $glob_look_poles=false $glob_h=c(0.001) $glob_display_interval=c(0.01) #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) x = c(x) return(c(10.0) * (c(0.1) * c(x) + c(0.2)) * arcsin(c(0.1) * c(x) + c(0.2) )+c(10.0) * sqrt(c(1.0) - expt((c(0.1) * c(x) + c(0.2)) , c(2) ))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 10.221321274539148 y[1] (numeric) 10.221321274539148 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 14 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.11000000000000001 y[1] (closed_form) 10.223442138547647 y[1] (numeric) 10.223442138543897 absolute error 3.749889287973929e-12 relative error 3.6679322259133384e-11% Desired digits 8 Estimated correct digits 13 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 0.12000000000000002 y[1] (closed_form) 10.225573232882073 y[1] (numeric) 10.225573232874543 absolute error 7.529976642217662e-12 relative error 7.363867502316387e-11% Desired digits 8 Estimated correct digits 13 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 0.13000000000000003 y[1] (closed_form) 10.22771455980771 y[1] (numeric) 10.227714559796388 absolute error 1.1322498494337196e-11 relative error 1.107040915947313e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] 0.14000000000000004 y[1] (closed_form) 10.229866121602074 y[1] (numeric) 10.229866121586936 absolute error 1.5138112985368934e-11 relative error 1.4797958062620465e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] 0.15000000000000005 y[1] (closed_form) 10.232027920554927 y[1] (numeric) 10.232027920535952 absolute error 1.8975043758473475e-11 relative error 1.854475369477332e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] 0.16000000000000006 y[1] (closed_form) 10.234199958968304 y[1] (numeric) 10.234199958945478 absolute error 2.282618538629322e-11 relative error 2.2303829784262193e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] 0.17000000000000007 y[1] (closed_form) 10.236382239156544 y[1] (numeric) 10.23638223912984 absolute error 2.6703972366703965e-11 relative error 2.6087314583227517e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] 0.18000000000000008 y[1] (closed_form) 10.238574763446298 y[1] (numeric) 10.238574763415697 absolute error 3.0601299272348115e-11 relative error 2.9888241263423404e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] 0.19000000000000009 y[1] (closed_form) 10.240777534176562 y[1] (numeric) 10.240777534142046 absolute error 3.451638974638627e-11 relative error 3.3704852616116955e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 Finished! diff ( y , x , 1 ) = arcsin ( 0.1 * x + 0.2 ) ; Iterations 100 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 101.00000000000009%