Solution of boundary value and eigenvalue problems for second order elliptic operators in the plane using pseudoanalytic formal powers

Details Solution of boundary value and eigenvalue problems for second order elliptic operators in the plane using pseudoanalytic formal powers Solution of boundary value and eigenvalue problems for second order elliptic operators in the plane using pseudoanalytic formal powers

2010-02-05

arxiv.org/abs/1002.1110v1

Mathematical Methods in the Applied Sciences, 2011, v. 34, issue 4, 455-468

Mathematics

Analysis of PDEs

Scientific paper

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.

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