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.

References in corpus (2)

• On a relation of pseudoanalytic function theory to the two-dimensional stationary Schroedinger equation and Taylor series in formal powers for its solutions
• On a factorization of second order elliptic operators and applications

Cited by in corpus (7)

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• First characterization of a new method for numerically solving the Dirichlet problem of the two-dimensional Electrical Impedance Equation
• Study of the forward Dirichlet boundary value problem for the two-dimensional Electrical Impedance Equation
• Study of the numerical solutions for the Electrical Impedance Equation in the plane: A pseudoanalytic approach of the forward Dirichlet boundary value problem
• Fundamentals of bicomplex pseudoanalytic function theory: Cauchy integral formulas, negative formal powers and Schrödinger equations with complex coefficients