Solution of boundary value and eigenvalue problems for second order elliptic operators in the plane using pseudoanalytic formal powers
Analysis of PDEs
2011-11-18 v1 Mathematical Physics
Complex Variables
math.MP
Numerical Analysis
Abstract
We propose a method for solving boundary value and eigenvalue problems for the elliptic operator D=divpgrad+q in the plane using pseudoanalytic function theory and in particular pseudoanalytic formal powers. Under certain conditions on the coefficients p and q with the aid of pseudoanalytic function theory a complete system of null solutions of the operator can be constructed following a simple algorithm consisting in recursive integration. This system of solutions is used for solving boundary value and spectral problems for the operator D in bounded simply connected domains. We study theoretical and numerical aspects of the method.
Keywords
Cite
@article{arxiv.1002.1110,
title = {Solution of boundary value and eigenvalue problems for second order elliptic operators in the plane using pseudoanalytic formal powers},
author = {Raul Castillo Perez and Vladislav V. Kravchenko and Rabindranath Resendiz Vazquez},
journal= {arXiv preprint arXiv:1002.1110},
year = {2011}
}