Open Access

ABSTRACT

General ray method for solution of the Dirichlet boundary value problems for elliptic partial differential equations in domains with complicated geometry

A. Grebennikov¹

1 FCFM BUAP, Puebla, Mexico

The International Conference on Computational & Experimental Engineering and Sciences 2010, 15(3), 85-90. https://doi.org/10.3970/icces.2010.015.085

Abstract

New General Ray (GR) method for solution of the Dirichlet boundary value problem for the class of elliptic Partial Differential Equations (PDE) is proposed. GR-method consists in application of the Radon transform directly to the PDE and in reduction PDE to assemblage of Ordinary Differential Equations (ODE). The class of the PDE includes the Laplace, Poisson and Helmgoltz equations. GR-method presents the solution of the Dirichlet boundary value problem for this type of equations by explicit analytical formulas that use the direct and inverse Radon transform. Proposed version of GR-method justified theoretically, realized by fast algorithms and MATLAB software, which quality we demonstrate by numerical experiments.

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