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

✍ Scribed by Raúl Castillo Pérez; Vladislav V. Kravchenko; Rabindranath Reséndiz Vázquez

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 262 KB
• Volume: 34
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1372

✦ Synopsis

Communicated by G. Franssens

We propose a method for solving boundary value and eigenvalue problems for the elliptic operator D = div p grad+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.