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/arcsin_sqrtpostode.ode################# diff ( y , x , 1 ) = arcsin ( 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(0.01) # 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) #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)) * arcsin(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) 0.609057172997581651357231305616823e0+/-0.801e-29 y[1] (numeric) 0.609057172997581651357231305616823e0+/-0.804e-29 absolute error 0.0e0+/-0.1605e-28 relative error 0.0e0+/-0.2635220585451298645367439539770178e-26% 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) 0.656043113063794083461680584699879e0+/-0.866e-29 y[1] (numeric) 0.6560427892521763911685639626399211e0+/-0.816e-29 absolute error 0.3238116176922931166220599579e-6+/-0.168e-28 relative error 0.4935828320490355520873688576042816e-4+/-0.256e-26% 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) 0.704256780209429731722967507083071e0+/-0.922e-29 y[1] (numeric) 0.7042561341557161278738863876375723e0+/-0.828e-29 absolute error 0.6460537136038490811194454987e-6+/-0.175e-28 relative error 0.9173553336777639537849789028356158e-4+/-0.248e-26% 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) 0.753677597766865417959152978198309e0+/-0.1e-28 y[1] (numeric) 0.7536766306074863491862403880152901e0+/-0.845e-29 absolute error 0.9671593790687729125901830189e-6+/-0.184e-28 relative error 0.1283253452052244320238979854080606e-3+/-0.244e-26% Desired digits 8 Estimated correct digits 13 Correct digits 6 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) 0.804286661477623978589849028335457e0+/-0.107e-28 y[1] (numeric) 0.8042853739486453885882236714913624e0+/-0.866e-29 absolute error 0.12875289785900016253568440946e-5+/-0.193e-28 relative error 0.1600833434467969115462677462263334e-3+/-0.239e-26% Desired digits 8 Estimated correct digits 13 Correct digits 6 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 ) = arcsin ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations 10 Total Elapsed Time 43 Seconds Elapsed Time(since restart) 41 Seconds Time to Timeout 19 Minutes 17 Seconds Percent Done 0.11e3+/-0.165e-28%