Error estimation. By indicating with Th and T2h two applications of the extended trapezoid rule with integration steps h and 2h, respectively, the error with step h is estimated [Pg.30]

Evaluate estimated error given h and 2h step sizes erra odeerror(si,s2) Evaluation of estimated error print(errstat(erra[2] ) ) statistics of error estimate print(errstat(erra[3])) returns statistics of errors [Pg.502]

Listing 12.35. Code for estimating error of PDE solution by h-2h algorithm. [Pg.878]

Figure 12.11. Estimated error in solutions for the tubular chemical reactor obtained by the h-2h algorithm at t = 20. Solid lines are solutions. Dotted curves are estimated errors. |

Figure 12.6. Comparison of exact error for diffusion equation with error estimate based upon the h-2h algorithm. Curves are very close near the peak errors for each solution. |

The last line above shows the estimated error to the solution obtained with the smallest step size as being simply (jj -y ) i. In terms of Figure 10.18 the first order estimate of the solution error is then simply 1/3 of the difference between the dotted curve and the solid curve. This is the error estimate of the most accurate solution with the largest number of data points. This technique of numerically estimating the global error of a solution will be referred to as the h-2h error estimation technique. [Pg.504]

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