Solving Mixed Boundary Value Problems using  Fourier Transform and Dual Integral Equations  Method

Abubakar Umar; Zilkarnaini S. Maishanu

doi:10.4314/cajost.v4i1.2

Authors

Abubakar Umar Department of Mathematics, Sokoto State University, Sokoto Nigeria
Zilkarnaini S. Maishanu Department of Planning, Research and Statistics, National Commission for colleges of Education (NCCE), Abuja, Nigeria

DOI:

https://doi.org/10.4314/cajost.v4i1.2

Keywords:

Boundary value problem, Laplace’s equation, Mixed boundary value problems, Fourier transform, Dual integral equations

Abstract

The research considered the solution of the system of dual integral equations
involving Fourier transform occurring in mixed boundary value problems for
Laplace’s equation with mixed Dirichlet-Neumann boundary conditions. The
dual integral equations involving trigonometric function kernel have been solved
using Fourier sine transforms. Graphical solutions with the help of Mathematica
were used to demonstrate the effectiveness of this method.