|
|||||
|
|
Solution of boundary and eigenvalue problems for second‐order elliptic operators in the plane using pseudoanalytic formal powers |
|
| Authors: | Raúl Castillo Pérez Vladislav V Kravchenko Rabindranath Reséndiz Vázquez |
| Institution: | 1. SEPI, ESIME Zacatenco, Instituto Politécnico Nacional, Av. IPN S/N, C.P. 07738, D.F. Mexico;2. Department of Mathematics, CINVESTAV del IPN, Unidad Queretaro, Libramiento Norponiente No. 2000, Fracc. Real de Juriquilla, Queretaro, Qro. C.P. 76230 Mexico |
| Abstract: | We propose a method for solving boundary value and eigenvalue problems for the elliptic operator D = div p grad + qin 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. Copyright © 2010 John Wiley & Sons, Ltd. |
| Keywords: | pseudoanalytic function Vekua equation Schrö dinger equation boundary value problem eigenvalue problem |