Initializing... Initialized Initializing(2)... PI = 0.3141592653589793238462643383279486e1+/-0.313e-31 E = 0.2718281828459045235360287471352649e1+/-0.256e-30 LOG_E_10 = 0.2302585092994045684017991454684277e1+/-0.5e-30 Initialized(2) ##############ECHO OF PROBLEM################# ##############temp/arccos_sqrtpostode.ode################# diff ( y , x , 1 ) = arccos ( sqrt ( 0.1 * x + 0.2 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.0) x_end=c(0.5) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=c(0.001) # 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]=c(-2.0) # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=c(0.5) # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=8 $glob_max_minutes=(20.0) $glob_subiter_method=3 $glob_max_iter=1000 $glob_upper_ratio_limit=c(1.11) $glob_lower_ratio_limit=c(0.99) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb #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)) * arccos(sqrt ( c(0.1) * c(x) + c(0.2))) - c(5.0) * sqrt( c(0.1) * c(x) + c(0.2)) * sqrt( c(0.8) - c(0.1) * c(x)) + c(5.0) * arcsin(sqrt( c(0.1) * c(x) + c(0.2)))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.0e0+/-0.50e-31 y[1] (closed_form) 0.2532535480592211587105412077662661e1+/-0.850e-29 y[1] (numeric) 0.2532535480592211587105412077662661e1+/-0.874e-29 absolute error 0.0e0+/-0.1724e-28 relative error 0.0e0+/-0.6807407095425401360989216899179635e-27% Desired digits 8 Estimated correct digits 14 Correct digits 32 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1999999999999999999999999999999974e1+/-0.503e-28 Order of pole (given) 0.5e0+/-0.50e-31 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] 0.1e0+/-0.2e-100 y[1] (closed_form) 0.264262917320548881692409496774358e1+/-0.918e-29 y[1] (numeric) 0.2642629497017106509217211589803536e1+/-0.98e-29 absolute error 0.323811617692293116622059956e-6+/-0.189e-28 relative error 0.1225338844267401015625189073069293e-4+/-0.715e-27% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.209999999999999999999999999999996e1+/-0.503e-28 Order of pole (given) 0.5e0+/-0.50e-31 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] 0.2e0+/-0.4e-100 y[1] (closed_form) 0.2751495138739342830585940214524362e1+/-0.976e-29 y[1] (numeric) 0.2751495784793056434435021333969858e1+/-0.102e-28 absolute error 0.646053713603849081119445496e-6+/-0.199e-28 relative error 0.2348009649400480500054440810738203e-4+/-0.723e-27% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.2199999999999999999999999999999949e1+/-0.503e-28 Order of pole (given) 0.5e0+/-0.50e-31 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] 0.3e0+/-0.6e-100 y[1] (closed_form) 0.2859153953861396806272886912573099e1+/-0.105e-28 y[1] (numeric) 0.2859154921020775875045799502756114e1+/-0.104e-28 absolute error 0.967159379068772912590183015e-6+/-0.209e-28 relative error 0.3382676815155711246400784441204813e-4+/-0.73e-27% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.2299999999999999999999999999999943e1+/-0.503e-28 Order of pole (given) 0.5e0+/-0.50e-31 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] 0.4e0+/-0.8e-100 y[1] (closed_form) 0.2965624522830127907565323031599924e1+/-0.113e-28 y[1] (numeric) 0.2965625810359106497566948388444015e1+/-0.106e-28 absolute error 0.1287528978590001625356844091e-5+/-0.219e-28 relative error 0.4341510426145581786445443746060791e-4+/-0.738e-27% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.2399999999999999999999999999999937e1+/-0.503e-28 Order of pole (given) 0.5e0+/-0.50e-31 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 ) = arccos ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations 10 Total Elapsed Time 46 Seconds Elapsed Time(since restart) 43 Seconds Time to Timeout 19 Minutes 14 Seconds Percent Done 0.11e3+/-0.165e-28%