95440 20201113085628.0 doi 10.1016/j.camwa.2019.08.038 sideral 114078 ART-2019-114078 eng (orcid)0000-0003-3570-0202 Llorente, Víctor J. Compact integration rules as a quadrature method with some applications 2019 Access copy available to the general public Unrestricted In many instances of computational science and engineering the value of a definite integral of a known function f(x) 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 ¿x1 x2f(x)dx 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 f(x). The coefficients that multiply both the integrals and f(x) 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. info:eu-repo/grantAgreement/ES/DGA-FEDER/Construyendo Europa desde Aragón info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 3.37 2019 MATHEMATICS, APPLIED 8 / 260 = 0.031 2019 Q1 T1 1.214 2019 Computational Mathematics 2019 Q1 Modeling and Simulation 2019 Q1 Computational Theory and Mathematics 2019 Q1 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion (orcid)0000-0003-1161-7893 Pascau, Antonio Universidad de Zaragoza 5001 600 Universidad de Zaragoza Dpto. Ciencia Tecnol.Mater.Fl. Área Mecánica de Fluidos 79, 5 (2019), 1241-1265 Comput. math. appl. COMPUTERS & MATHEMATICS WITH APPLICATIONS 0898-1221 672350 http://zaguan.unizar.es/record/95440/files/texto_completo.pdf Postprint 251202 http://zaguan.unizar.es/record/95440/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:95440 articulos driver 2020-11-13-08:47:38 ARTICLE