Non-Iterative Solution Methods for Cauchy Problems for Laplace and Helmholtz Equation in Annulus Domain

Mohsen Tadi and Miloje Radenkovic
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Mohsen Tadi: Department of Engineering, Central Connecticut State University, New Britain, CT 06053, USA
Miloje Radenkovic: Department of Electrical Engineering, University of Colorado Denver, Denver, CO 80204, USA

Mathematics, 2021, vol. 9, issue 3, 1-14

Abstract: This note is concerned with two new methods for the solution of a Cauchy problem. The first method is based on homotopy-perturbation approach which leads to solving a series of well-posed boundary value problems. No regularization is needed in this method. Laplace and Helmholtz equations are considered in an annular region. It is also proved that the homotopy solution for the Laplace operator converges to the actual exact solution. The second method is also non-iterative. It is based on the application of the Green’s second identity which leads to a moment problem for the unknown boundary condition. Tikhonov regularization is used to obtain a stable and close approximation of the missing boundary condition. A number of examples are used to study the applicability of the methods with the presence of noise.

Keywords: Cauchy problem; Homotopy perturbation; moment problem; Helmholtz equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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