Fast Algorithms and MATLAB Software for Solution of the Dirichlet Boundary Value Problems for Elliptic Partial Differential Equations in Domains with Complicated Geometry
نویسنده
چکیده
New fast algorithms for solution of the Dirichlet boundary value problem for the class of elliptic Partial Differential Equations (PDE) is proposed. Algorithms are based on new version of General Ray (GR) method which 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 is justified theoretically, realized by MATLAB software, which quality we demonstrate by numerical experiments. Key-Words: fast algorithms, boundary value problems , partial differential equations, Radon transform, MATLAB software
منابع مشابه
General ray method for solution of the Dirichlet boundary value problems for elliptic partial differential equations in domains with complicated geometry
New General Ray (GR) method for solution of the Dirichlet boundary value problem for the class of elliptic Partial Differential Equations (PDE) is proposed. GRmethod 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. GRmethod pr...
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