| Author's Name: |
M. A. Abdou & M. A. Elsayed |
| Subject Area: |
Science and Engineering |
| Subject |
Mathematics |
| Section |
Research Paper |
Keyword:
Mixed integral equation, system of Fredholm integral equations, Krein s method, spectral relationships, Chebyshev polynomials (CPs).
Abstract
In this paper, the existence of a unique solution of mixed integral equation (MIE) of the first kind is considered in the
space L2 [-1, 1 ]*C(0,T ) , T< 1. The integral term of position, in L2 [-1, 1], has a discontinuous kernel, while the
integral term of time, in C (0,T ), has a continuous kernel. Using a numerical, we have system of Fredholm integral
equations (SFIEs) of the first find. Then, using Krein s method, the solution of the integral system is obtained in the form
of spectral relationships (SRs) of eigenvalues and eigenfunctions. Many special cases are considered and many
applications in fluid mechanics and contact problems are discussed.