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