BOUNDARY AND INITIAL VALUE PROBLEMS AND INTEGRAL OPERATOR

In this paper, we consider an initial value problem of integrodifferential type (IVP). This kind of problem transforms into Fredholm-Volterra integral equation of second kind (F-VIESK). We discuss the existence of a unique solution of the problem by using Banach fixed point theorem. On the other hand, we reduce the boundary value problems of integrodifferential type (BVP) to Fredholm integral equation of second kind (FIESK). Then we use the Chebyshev-Legendre collocation method to solve the (IVP) and (BVP) when both the kernel function and the source function are sufficiently smooth. Some numerical results are obtained by using the MATLAB 2017 program. Then we plot the different relations between the analytic solutions and the approximate solutions and between the two approximate errors.