Introduction to Shannon sampling and interpolation theory
Introduction to Shannon sampling and interpolation theory
A finite difference scheme for partial integro-differential equations with a weakly singular kernel
Applied Numerical Mathematics
An introduction to wavelets
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Journal of Computational Physics
SIAM Journal on Scientific Computing
DSC time-domain solution of Maxwell's equations
Journal of Computational Physics
Adomian decomposition method for solving BVPs for fourth-order integro-differential equations
Journal of Computational and Applied Mathematics
A Space-Time Spectral Method for the Time Fractional Diffusion Equation
SIAM Journal on Numerical Analysis
Analysis of a Local Discontinuous Galerkin Method for Linear Time-Dependent Fourth-Order Problems
SIAM Journal on Numerical Analysis
Numerical solution of fourth-order integro-differential equations using Chebyshev cardinal functions
International Journal of Computer Mathematics
Journal of Computational and Applied Mathematics
A Legendre Petrov-Galerkin method for fourth-order differential equations
Computers & Mathematics with Applications
Computers & Mathematics with Applications
International Journal of Computer Mathematics
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In this paper, we study a novel numerical scheme for the fourth order partial integro-differential equation with a weakly singular kernel. In the time direction, a Crank-Nicolson time-stepping is used to approximate the differential term and the product trapezoidal method is employed to treat the integral term, and the quasi-wavelets numerical method for space discretization. Our interest in the present paper is a continuation of the investigation in Yang et al. [33], where we study discretization in time by using the forward Euler scheme. The comparisons of present results with the previous ones show that the present scheme is more stable and efficient for numerically solving the fourth order partial integro-differential equation with a weakly singular kernel. We also tested the method proposed on several one and two dimensional problems with very promising results. Besides, in order to demonstrate the power of the quasi-wavelets method in comparison with standard discretization methods we also consider the high-frequency oscillation problems with the integro-differential term.