Legendre and Chebyshev Polynomials for Solving Mixed Integral Equation

In this paper, the solution of mixed integral equation (MIE) of the first and second kind in time and position is discussed and obtained in the space L2[-1,1]x C[o,T],T < 1. The kernel of position is established in the logarithmic form, while the kernels of time are continuous and positive functions in C[0,T]. A numerical method is used to obtain a linear system of Fredholm integral equations (SFIEs). In addition, the solution FIE of the second kind, with singular kernel, is solved, using Legendre polynomials. Moreover, Orthogonal polynomials methods are used to obtain the solution of singular FIE of the first kind.