Extrapolation method for solving two-dimensional volterral integral equations of the second kind

In this paper, we propose a numerical quadrature method for solving two-dimensional linear and nonlinear Volterra integral equations. Firstly, we generalize one-dimensional quadrature formula to two-dimensional case and its corresponding error asymptotic expansion. Based on the quadrature formula an...

Full description

Saved in:
Bibliographic Details
Published in:Applied mathematics and computation 2020-02, Vol.367, p.124784, Article 124784
Main Authors: Pan, Yubin, Huang, Jin
Format: Article
Language:English
Subjects:
Asymptotic expansion
Error analysis
Extrapolation algorithm
Iterative scheme
Quadrature formula
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we propose a numerical quadrature method for solving two-dimensional linear and nonlinear Volterra integral equations. Firstly, we generalize one-dimensional quadrature formula to two-dimensional case and its corresponding error asymptotic expansion. Based on the quadrature formula and the error expansion, we next construct an iterative scheme and extrapolation algorithm. The numerical solution of any point can be calculated by iterative scheme, and the error accuracy and convergence order of the numerical solution are further improved by extrapolation algorithm. Using the extrapolation algorithm, we can improve the convergence order from O(h02) to O(h03) or even O(h04). Since, the numerical solution of each point is obtained by assignment operation and iteration, the computational complexity can be greatly reduced. Finally, four numerical examples are given to illustrate the effectiveness of the method.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2019.124784