Affiliation:
1. Benha University, Benha, Egypt Alexandria University, Alexandria, Egypt
Abstract
In this paper, we discussed the existence and uniqueness of solution of the
singular Quadratic integral equation (SQIE). The Fredholm integral term is assumed in
position with singular kernel. Under certain conditions and new discussions, the singular
kernel will tend to a logarithmic kernel. Then, using Chebyshev polynomial, a main of
spectral relationships are stated and used to obtain the solution of the singular Quadratic
integral equation with the logarithmic kernel and a smooth kernel. Finally, the Fredholm
integral equation of the second kind is established and its solution is discussed, also numerical results are obtained and the error, in each case, is computed.
Publisher
National Academy of Sciences of the Republic of Armenia