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Journal of Advances in Mathematics and Computer Science, ISSN: 2456-9968, ISSN: 2231-0851 (Past),Vol.: 30, Issue.: 1


Solution to the Dirichlet Problem on Irregular Domains Using Wavelet-Based Approach


Francis Ohene Boateng1*, Joseph Ackora-Prah2 and Anthony Y. Aidoo3

1Department of Mathematics Education, University of Education, Winneba, Kumasi, Ghana.

2Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.

3Department of Mathematics and Computer Science, Eastern Connecticut State University, Willimantic, USA.

Article Information
(1) Dr. Dragos-Patru Covei, Professor, Department of Applied Mathematics, The Bucharest University of Economic Studies, Piata Romana, Romania.
(1) Omenyi, O. Louis, Alex Ekwueme Federal University, Nigeria.
(2) Nalini V .Vaidya, G H Raisoni College of Engineering Nagpur, India.
(3) Oluleye (H) Babatunde, Charleston Southern University, USA.
(4) Njoseh, Ignatius Nkonyeasua, Delta State University, Nigeria.
Complete Peer review History: http://www.sciencedomain.org/review-history/28010


We present a Finite Difference Fictitious Domain Wavelet Method (FDFDWM) with penalty for solving two dimensional (2D) Dirichlet problem for linear elliptic PDE on irregular geometric domains. In this method, the 2-D Dirichlet problem is discretized along one of the spatial variables, reducing it to a 1-D problem. The problem and the boundaries of the irregular domain are approximated using compactly supported wavelets. Results from the numerical analysis indicate that, our method performs better in terms of accuracy and convergence of the approximate solution compared with finite element method.

Keywords :

Dirichlet problem; penalty; fictitious domain; PDEs; Daubechies wavelet function; irregular domain; finite difference.

Full Article - PDF    Page 1-14

DOI : 10.9734/JAMCS/2019/45965

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