A Finite Difference Fictitious Domain Wavelet Method for Solving Dirichlet Boundary Value Problem

  • Francis Ohene Boateng Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development, Kumasi https://orcid.org/0000-0003-0197-7385
  • Joseph Ackora-Prah
  • Benedict Barnes
  • John Amoah-Mensah
Keywords: fictitious domain, Dirichlet problem, wavelet, finite difference, finite element

Abstract

In this paper, we introduce a Finite Difference Fictitious Domain Wavelet Method (FDFDWM) for solving two dimensional (2D) linear elliptic  partial differential equations (PDEs) with Dirichlet boundary conditions on regular geometric domain. The method reduces the 2D PDE into a 1D system of ordinary differential equations and applies a compactly supported wavelet to approximate the solution. The problem is embedded in a fictitious domain to aid the enforcement of the Dirichlet boundary conditions. We present numerical analysis and show that our method yields better approximation to the solution of the Dirichlet problem than traditional methods like the finite element and finite difference methods.

Author Biography

Francis Ohene Boateng, Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development, Kumasi

Department of Mathematics Education

Senior Lecturer

Published
2021-08-05
Section
Nonlinear Analysis