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

摘要

We propose a method for solving boundary value and eigenvalue problems forthe elliptic operator D=divpgrad+q in the plane using pseudoanalytic functiontheory and in particular pseudoanalytic formal powers. Under certain conditionson the coefficients p and q with the aid of pseudoanalytic function theory acomplete system of null solutions of the operator can be constructed followinga simple algorithm consisting in recursive integration. This system ofsolutions is used for solving boundary value and spectral problems for theoperator D in bounded simply connected domains. We study theoretical andnumerical aspects of the method.