TY  - EJOU
AU  - Grebennikov, A. 

TI  - General ray method for solution of the Dirichlet boundary value problems for elliptic partial differential equations in domains with complicated geometry
T2  - The International Conference on Computational \& Experimental Engineering and Sciences

PY  - 2010
VL  - 15
IS  - 3
SN  - 1933-2815

AB  - New General Ray (<i>GR</i>) method for solution of the Dirichlet boundary value problem for the class of elliptic Partial Differential Equations (PDE) is proposed. <i>GR</i>-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. <i>GR</i>-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 <i>GR</i>-method justified theoretically, realized by fast algorithms and MATLAB software, which quality we demonstrate by numerical experiments.
KW  - partial differential equations
KW  -  boundary value problems
KW  -  Radon transform
KW  -  fast algorithms
KW  -  MATLAB software

DO  - 10.3970/icces.2010.015.085