000095440 001__ 95440 000095440 005__ 20201113085628.0 000095440 0247_ $$2doi$$a10.1016/j.camwa.2019.08.038 000095440 0248_ $$2sideral$$a114078 000095440 037__ $$aART-2019-114078 000095440 041__ $$aeng 000095440 100__ $$0(orcid)0000-0003-3570-0202$$aLlorente, Víctor J. 000095440 245__ $$aCompact integration rules as a quadrature method with some applications 000095440 260__ $$c2019 000095440 5060_ $$aAccess copy available to the general public$$fUnrestricted 000095440 5203_ $$aIn many instances of computational science and engineering the value of a definite integral of a known function f(x) is required in an interval. Nowadays there are plenty of methods that provide this quantity with a given accuracy. In one way or another, all of them assume an interpolating function, usually polynomial, that represents the original function either locally or globally. This paper presents a new way of calculating ¿x1 x2f(x)dx by means of compact integration, in a similar way to the compact differentiation employed in computational physics and mathematics. Compact integration is a linear combination of definite integrals associated to an interval and its adjacent ones, written in terms of nodal values of f(x). The coefficients that multiply both the integrals and f(x) at the nodes are obtained by matching terms in a Taylor series expansion. In this implicit method a system of algebraic equations is solved, where the vector of unknowns contains the integrals in each interval of a uniform discrete domain. As a result the definite integral over the whole domain is the sum of all these integrals. In this paper the mathematical tool is analyzed by deriving the appropriate coefficients for a given accuracy, and is exploited in various numerical examples and applications. The great accuracy of the method is highlighted. 000095440 536__ $$9info:eu-repo/grantAgreement/ES/DGA-FEDER/Construyendo Europa desde Aragón 000095440 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000095440 590__ $$a3.37$$b2019 000095440 591__ $$aMATHEMATICS, APPLIED$$b8 / 260 = 0.031$$c2019$$dQ1$$eT1 000095440 592__ $$a1.214$$b2019 000095440 593__ $$aComputational Mathematics$$c2019$$dQ1 000095440 593__ $$aModeling and Simulation$$c2019$$dQ1 000095440 593__ $$aComputational Theory and Mathematics$$c2019$$dQ1 000095440 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000095440 700__ $$0(orcid)0000-0003-1161-7893$$aPascau, Antonio$$uUniversidad de Zaragoza 000095440 7102_ $$15001$$2600$$aUniversidad de Zaragoza$$bDpto. Ciencia Tecnol.Mater.Fl.$$cÁrea Mecánica de Fluidos 000095440 773__ $$g79, 5 (2019), 1241-1265$$pComput. math. appl.$$tCOMPUTERS & MATHEMATICS WITH APPLICATIONS$$x0898-1221 000095440 8564_ $$s672350$$uhttps://zaguan.unizar.es/record/95440/files/texto_completo.pdf$$yPostprint 000095440 8564_ $$s251202$$uhttps://zaguan.unizar.es/record/95440/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000095440 909CO $$ooai:zaguan.unizar.es:95440$$particulos$$pdriver 000095440 951__ $$a2020-11-13-08:47:38 000095440 980__ $$aARTICLE