An Asymptotic Model for Solving Mixed Integral Equation in Position and Time

In this paper, we considered a mixed integral equation (MIE) of the second kind in space L 2 ? b , × C 0 T < 1. The kernel position has singularity and takes some different famous forms, while kernels time are positive continuous. Using an asymptotic method separating variables, have Fredholm (FIE) with variable parameters time. Then, using Toeplitz matrix (TMM), obtain linear algebraic system (LAS) that can be solved numerically. Some applications aid maple 18 program discussed when Coleman function, Cauchy kernel, Hilbert generalized logarithmic function. Also error estimate, each case, is computed.