##############ECHO OF PROBLEM################# ##############temp/cosh_sqrtpostode.ode################# diff ( y , x , 1 ) = cosh ( 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(-1.9) x_end=c(-1.8) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=0.01 $glob_upper_ratio_limit=c(1.001) $glob_lower_ratio_limit=c(0.999) # 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=(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=true $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(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * sinh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * cosh( 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] -1.9 y[1] (closed_form) -19.899749861076383 y[1] (numeric) -19.899749861076383 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 14 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.10000000000000009 Order of pole (given) 0.5 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] -1.890000000000001 y[1] (closed_form) -19.889697315088046 y[1] (numeric) -19.88969756592337 absolute error 2.508353240671113e-07 relative error 1.261131932243288e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 Radius of convergence (given) for eq 1 0.10999999999999899 Order of pole (given) 0.5 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] -1.8800000000000021 y[1] (closed_form) -19.87963975992799 y[1] (numeric) -19.87964026160569 absolute error 5.01677700270875e-07 relative error 2.523575408454445e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 Radius of convergence (given) for eq 1 0.11999999999999789 Order of pole (given) 0.5 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] -1.8700000000000032 y[1] (closed_form) -19.869577194761927 y[1] (numeric) -19.86957794729463 absolute error 7.525327028190532e-07 relative error 3.787361429197587e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 Radius of convergence (given) for eq 1 0.12999999999999678 Order of pole (given) 0.5 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] -1.8600000000000043 y[1] (closed_form) -19.859509618755478 y[1] (numeric) -19.859510622160133 absolute error 1.0034046553641929e-06 relative error 5.052514763086444e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 Radius of convergence (given) for eq 1 0.13999999999999568 Order of pole (given) 0.5 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] -1.8500000000000054 y[1] (closed_form) -19.84943703107419 y[1] (numeric) -19.849438285371157 absolute error 1.2542969685114258e-06 relative error 6.319055631390606e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 Radius of convergence (given) for eq 1 0.14999999999999458 Order of pole (given) 0.5 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] -1.8400000000000065 y[1] (closed_form) -19.839359430883512 y[1] (numeric) -19.839360936095943 absolute error 1.5052124311409898e-06 relative error 7.58700116495625e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 Radius of convergence (given) for eq 1 0.15999999999999348 Order of pole (given) 0.5 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] -1.8300000000000076 y[1] (closed_form) -19.829276817348823 y[1] (numeric) -19.82927857350212 absolute error 1.7561532956733572e-06 relative error 8.856365826397068e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 Radius of convergence (given) for eq 1 0.16999999999999238 Order of pole (given) 0.5 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] -1.8200000000000087 y[1] (closed_form) -19.819189189635416 y[1] (numeric) -19.819191196756844 absolute error 2.0071214272832094e-06 relative error 1.0127162156224068e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 Radius of convergence (given) for eq 1 0.17999999999999128 Order of pole (given) 0.5 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] -1.8100000000000098 y[1] (closed_form) -19.809096546908492 y[1] (numeric) -19.8090988050269 absolute error 2.2581184069281335e-06 relative error 1.1399401288094317e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 Radius of convergence (given) for eq 1 0.18999999999999018 Order of pole (given) 0.5 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] -1.800000000000011 y[1] (closed_form) -19.798998888333184 y[1] (numeric) -19.79900139747874 absolute error 2.509145556217618e-06 relative error 1.2673093070863115e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 Radius of convergence (given) for eq 1 0.19999999999998908 Order of pole (given) 0.5 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 ) = cosh ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations 101 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 101.9999999999889%