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

arXiv eprints
 Pub Date:
 February 2010
 arXiv:
 arXiv:1002.1110
 Bibcode:
 2010arXiv1002.1110C
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 Mathematics  Complex Variables;
 Mathematics  Numerical Analysis;
 30G20;
 35J25;
 65N25
 EPrint:
 Mathematical Methods in the Applied Sciences, 2011, v. 34, issue 4, 455468