##############ECHO OF PROBLEM################# ##############temp/expt_sin_cpostode.ode################# diff ( y , x , 1 ) = expt ( sin ( 0.2 * x + 0.3 ) , 2.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.1) x_end=c(0.2) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true #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(-2.5000000000000000000000000000000)*sin(c(0.20000000000000000000000000000000)*c(x)+c(0.30000000000000000000000000000000))*cos(c(0.20000000000000000000000000000000)*c(x)+c(0.30000000000000000000000000000000))+c(0.50000000000000000000000000000000)*c(x)+c(0.75000000000000000000000000000000)) 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) 0.05350569829701002 y[1] (numeric) 0.05350569829701002 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 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] 0.11000000000000001 y[1] (closed_form) 0.05450120214864118 y[1] (numeric) 0.05450120202857519 absolute error 1.2006599187097677e-10 relative error 2.2029971291921357e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 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] 0.12000000000000002 y[1] (closed_form) 0.05550871396502721 y[1] (numeric) 0.055508713725055434 absolute error 2.3997177855950014e-10 relative error 4.3231370611593036e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 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] 0.13000000000000003 y[1] (closed_form) 0.056528297625894064 y[1] (numeric) 0.056528297266177356 absolute error 3.597167078095431e-10 relative error 6.363480290706061e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 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] 0.14000000000000004 y[1] (closed_form) 0.05756001681781808 y[1] (numeric) 0.057560016338518316 absolute error 4.792997665425958e-10 relative error 8.32695668000961e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 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] 0.15000000000000005 y[1] (closed_form) 0.05860393503320782 y[1] (numeric) 0.05860393443448743 absolute error 5.987203927082518e-10 relative error 1.0216385510102485e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 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] 0.16000000000000006 y[1] (closed_form) 0.059660115569287187 y[1] (numeric) 0.059660114851309703 absolute error 7.179774830223806e-10 relative error 1.2034463496614358e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 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] 0.17000000000000007 y[1] (closed_form) 0.06072862152708347 y[1] (numeric) 0.060728620690013266 absolute error 8.370702048177137e-10 relative error 1.378378405056339e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 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] 0.18000000000000008 y[1] (closed_form) 0.0618095158104176 y[1] (numeric) 0.06180951485441977 absolute error 9.55997836449285e-10 relative error 1.5466839109070605e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 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] 0.19000000000000009 y[1] (closed_form) 0.06290286112489729 y[1] (numeric) 0.0629028600501379 absolute error 1.07475939259416e-09 relative error 1.7086017605147765e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 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 ) = expt ( sin ( 0.2 * x + 0.3 ) , 2.0 ) ; 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%