A Finite Difference Fictitious Domain Wavelet Method for Solving Dirichlet Boundary Value Problem
DOI:
https://doi.org/10.29020/nybg.ejpam.v14i3.3893Keywords:
fictitious domain, Dirichlet problem, wavelet, finite difference, finite elementAbstract
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.Downloads
Published
2021-08-05
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How to Cite
A Finite Difference Fictitious Domain Wavelet Method for Solving Dirichlet Boundary Value Problem. (2021). European Journal of Pure and Applied Mathematics, 14(3), 706-722. https://doi.org/10.29020/nybg.ejpam.v14i3.3893