Solution of boundary value and eigenvalue problems for second order elliptic operators in the plane using pseudoanalytic formal powers
It provides a new computational approach for elliptic boundary value problems, but the method is demonstrated only in 2D and for specific domains, making it incremental for applied mathematics.
The paper proposes a method for solving boundary value and eigenvalue problems for second order elliptic operators in the plane using pseudoanalytic formal powers, enabling construction of null solutions via recursive integration. Numerical results are presented for bounded simply connected domains.
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.