Paper Info
Title
Crank-Nicolson/quasi-wavelets method for solving fourth order partial integro-differential equation with a weakly singular kernel
Abstract
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.
Year
DOI
Venue
2013
10.1016/j.jcp.2012.09.037
J. Comput. Physics
Keywords
Field
DocType
quasi-wavelets method,integral term,differential term,quasi-wavelets numerical method,standard discretization method,weakly singular kernel,euler scheme,product trapezoidal method,order partial integro-differential equation,integro-differential term,integro differential equation
Discretization,Mathematical optimization,Mathematical analysis,Singular solution,Continuation,Trapezoidal rule,Integro-differential equation,Numerical analysis,Mathematics,Crank–Nicolson method,Wavelet
Journal
Volume
ISSN
Citations 
234,
0021-9991
5
PageRank 
References 
Authors
0.51
13
3
Name
Order
Citations
PageRank
Xuehua Yang1455.38
Da. Xu27411.27
Haixiang Zhang36412.19