Numerical solution of the fourth-order partial integro-differential equation with multi-term kernels by the Sinc-collocation method based on the double exponential transformation

Abstract

In this work, we consider a Sinc-collocation method for solving the fourth-order partial integro-differential equation with the multi-term kernels. In the temporal direction, the time derivative is approximated by the backward-Euler method and the first-order convolution quadrature is used for the discretization of the Riemann-Liouville (R-L) fractional integral terms. Then a fully discrete scheme is constructed with the discretization of space via the Sinc approximation based on the double exponential (DE) transformation. The convergence analysis of proposed method is obtained. Some numerical examples are given to demonstrate the effectiveness of our method. Meanwhile, the results via employing the single exponential (SE) transformation are provided to be compared with our method in order to manifest the high accuracy and efficiency of the proposed method.