Solving mixed boundary value problems using dual integral equations and dual series solution

Abstract

Dual integral equations arise when integral transforms are used to solve mixed boundary value problems of mathematical physics and mechanics. A formal technique for solving such equations have been developed. In specific mixed boundary value problems, Fourier transforms are applied, and subsequently, dual integral equations involving Bessel and trigonometric functions have been obtained. The present work aims to consider solvability and solution of systems of dual integral equations involving Fourier transform occurring in mixed boundary value problems for the Laplace’s equation with mixed Dirichlet-Neumann boundary conditions. The use of Abel’s integral transform was employed. Furthermore, Mathematica software has been used to obtain graphical solutions to the problems.