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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.
35J25Second order elliptic equations, boundary value problems
35P05General topics in linear spectral theory of PDE
35J10Schrödinger operator
31A25Boundary value and inverse problems (two-dimensional potential theory)
30G20Generalizations of analytic functions of Bers or Vekua type
30E25Boundary value problems, complex analysis