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Compact Integration Rules as a quadrature method with some applications

AuthorsLlorente, Víctor J.; Pascau, Antonio
KeywordsNumerical integration
Definite integral
Ordinary differential equations
The ENATE scheme
Issue Date1-Mar-2020
CitationComputers and Mathematics with Applications 79(5): 1241-1265 (2020)
AbstractIn many instances of computational science and engineering the value of a definite integral of a known function is required in an interval. Nowadays there are plenty of methods that provide this quantity with a given accuracy. In one way or another, all of them assume an interpolating function, usually polynomial, that represents the original function either locally or globally. This paper presents a new way of calculating by means of compact integration, in a similar way to the compact differentiation employed in computational physics and mathematics. Compact integration is a linear combination of definite integrals associated to an interval and its adjacent ones, written in terms of nodal values of . The coefficients that multiply both the integrals and at the nodes are obtained by matching terms in a Taylor series expansion. In this implicit method a system of algebraic equations is solved, where the vector of unknowns contains the integrals in each interval of a uniform discrete domain. As a result the definite integral over the whole domain is the sum of all these integrals. In this paper the mathematical tool is analyzed by deriving the appropriate coefficients for a given accuracy, and is exploited in various numerical examples and applications. The great accuracy of the method is highlighted.
Publisher version (URL)https://doi.org/10.1016/j.camwa.2019.08.038
Appears in Collections:(LFSPyN) Artículos
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