General Ray Method and Computer Program Package for Explicit Solution of Boundary Value Problems for Elliptic Partial Differential Equations in Domains with Complicated Geometry

摘要

A new version of General Ray (GR) method for solution of the Dirichlet boundary value problem for the class of elliptic Partial Differential Equations (PDE) is proposed. This version is based on application of the Radon transform directly to the PDE and consists in reduction PDE to assemblage of 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 is justified theoretically, realized by fast algorithms and MATLAB software, which quality is demonstrated by numerical experiments.