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Solution of boundary and eigenvalue problems for second-order elliptic operators in the plane using pseudoanalytic formal powers. (English) Zbl 1210.35054
Summary: 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.
##### MSC:
 35J25 Second order elliptic equations, boundary value problems 35P05 General topics in linear spectral theory of PDE 35J10 Schrödinger operator 31A25 Boundary value and inverse problems (two-dimensional potential theory) 30G20 Generalizations of analytic functions of Bers or Vekua type 30E25 Boundary value problems, complex analysis