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Resolución de ecuaciones diferenciales en derivadas parciales dependientes del tiempo de segundo orden utilizando diferencias finitas generalizadas

Revista internacional de métodos numéricos para cálculo y diseño en ingeniería; Vol.: 19 Núm.: 3
Source: OAI

ABSTRACT En este artículo se muestra la eficiencia del método de diferencias finitas generalizadas (MDFG) en la resolución , por el método explícito, de ecuaciones diferenciales en derivadas parciales dependientes del tiempo de segundo orden para una o dos dimensiones espaciales. La obtención de fórmulas explícitas en diferencias finitas generalizadas permite establecer un sencillo criterio de estabilidad, que viene expresado en función de los coeficientes de la ecuación de la estrella.

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    ABSTRACT: Classical finite difference schemes are in wide use today for approximately solving partial differential equations of mathematical physics. An evolution of the method of finite differences has been the development of generalized finite difference (GFD) method, that can be applied to irregular grids of points.In this paper the extension of the GFD to the explicit solution of parabolic and hyperbolic equations has been developed for partial differential equations with constant coefficients in the cases of considering one, two or three space dimensions. The convergence of the method has been studied and the truncation errors over irregular grids are given.Different examples have been solved using the explicit finite difference formulae and the criterion of stability. This has been expressed in function of the coefficients of the star equation for irregular clouds of nodes in one, two or three space dimensions. The numerical results show the accuracy obtained over irregular grids. This paper also includes the study of the maximum local error and the global error for different examples of parabolic and hyperbolic time-dependent equations.
    Journal of Computational and Applied Mathematics 01/2007; · 0.99 Impact Factor

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