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ENCIT 2020
18th Brazilian Congress of Thermal Sciences and Engineering
Truncation Error for the Simpson’s 1/3 Rule Based on Taylor Series Expansion
Submission Author:
Antonio Carlos Foltran , PR
Co-Authors:
Antonio Carlos Foltran, Carlos Henrique Marchi, Luís Mauro Moura
Presenter: Antonio Carlos Foltran
doi://10.26678/ABCM.ENCIT2020.CIT20-0167
Abstract
This paper presents a deduction of the truncation error for the Simpson’s 1/3 Rule as a series that can be used to code verification. Instead of using the classical approach of integration of interpolating polynomials, it uses the integration of the function expanded in Taylor Series. As result, the series is truncated after some terms. In this paper, it is deduced up to the third term. As well known, the Simpson’s 1/3 Rule has asymptotic order four, and the deduction presented here allows to conclude that the true orders constitute the arithmetic progression: 4, 6, 8, … By using Repeated Richardson Extrapolation, the apparent orders of the truncation error are confirmed a posteriori by testing polynomials and exponential functions. In addition, the deduced equation is able to calculate the truncation error exactly for all tested functions that has a finite number of non-null derivatives.
Keywords
Simpson’s 1/3 Rule, Truncation Error, Repeated Richardson Extrapolation, Error Equation, Code Verification, Solution Verification
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