Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 209, Issue 2, Pages 208-233Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2006.10.090
Keywords
parabolic equations; hyperbolic equations; generalized finite differences; irregular grids; explicit method
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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. (C) 2006 Elsevier B.V. All rights reserved.
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