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

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.

Keywords:   Boundary value problem; Laplace’s equation; Mixed boundary value problems; Fourier transform; Dual integral equations.