##############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; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-0.8); x_end=c(0.8); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=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); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double 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 USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -0.8 y[1] (closed_form) = 10.07208677566643 y[1] (numeric) = 10.07208677566643 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 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] = -0.7 y[1] (closed_form) = 10.08461961211218 y[1] (numeric) = 10.08461955934037 absolute error = 5.277181003293663e-08 relative error = 5.232900403060794e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.05 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] = -0.5999999999999999 y[1] (closed_form) = 10.09816101618305 y[1] (numeric) = 10.09816090615056 absolute error = 1.100324862335356e-07 relative error = 1.089628953798621e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 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] = -0.4999999999999998 y[1] (closed_form) = 10.11271237580762 y[1] (numeric) = 10.11271220397152 absolute error = 1.718361080094155e-07 relative error = 1.699208892962234e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 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] = -0.3999999999999999 y[1] (closed_form) = 10.12827518812551 y[1] (numeric) = 10.12827494988402 absolute error = 2.382414852064585e-07 relative error = 2.352241430858585e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 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] = -0.2999999999999999 y[1] (closed_form) = 10.14485106091358 y[1] (numeric) = 10.14485075160126 absolute error = 3.093123233099959e-07 relative error = 3.048958742250289e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 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] = -0.1999999999999999 y[1] (closed_form) = 10.16244171413014 y[1] (numeric) = 10.16244132901275 absolute error = 3.851173833169241e-07 relative error = 3.789614682674602e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 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] = -0.09999999999999991 y[1] (closed_form) = 10.18104898158115 y[1] (numeric) = 10.18104851585047 absolute error = 4.657306842403841e-07 relative error = 4.574486234993581e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 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] = 9.71445146547012e-17 y[1] (closed_form) = 10.20067481271337 y[1] (numeric) = 10.20067426148166 absolute error = 5.512317144962253e-07 relative error = 5.403874984909925e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 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] = 0.1000000000000001 y[1] (closed_form) = 10.22132127453915 y[1] (numeric) = 10.2213206328335 absolute error = 6.417056486185402e-07 relative error = 6.278108586773415e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 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] = 0.2000000000000001 y[1] (closed_form) = 10.24299055369871 y[1] (numeric) = 10.24298981645511 absolute error = 7.37243601278692e-07 relative error = 7.197542528363223e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 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] = 0.3000000000000001 y[1] (closed_form) = 10.26568495866573 y[1] (numeric) = 10.26568412072284 absolute error = 8.379428919624843e-07 relative error = 8.162561926811701e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 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] = 0.4000000000000001 y[1] (closed_form) = 10.28940692210279 y[1] (numeric) = 10.28940597819545 absolute error = 9.439073416217525e-07 relative error = 9.173583558000167e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 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] = 0.5000000000000001 y[1] (closed_form) = 10.31415900337374 y[1] (numeric) = 10.31415794812615 absolute error = 1.055247587089525e-06 relative error = 1.023105797326138e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.05 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] = 0.6000000000000002 y[1] (closed_form) = 10.33994389122067 y[1] (numeric) = 10.33994271913925 absolute error = 1.172081418587823e-06 relative error = 1.133547174838155e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.05 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] = 0.7000000000000003 y[1] (closed_form) = 10.3667644066138 y[1] (numeric) = 10.36676311207965 absolute error = 1.294534154538951e-06 relative error = 1.248734999430548e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.05 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 ) = arcsin ( 0.1 * x + 0.2 ) ; Iterations = 32 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 103.1 %