 Extrapolation method for solving two-dimensional volterral integral equations of the second kindYubin Pan and Jin Huang Applied Mathematics and Computation, 2020, vol. 367, issue C Abstract: 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. Keywords: Quadrature formula; Asymptotic expansion; Extrapolation algorithm; Iterative scheme; Error analysis (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:367:y:2020:i:c:s0096300319307763 DOI: 10.1016/j.amc.2019.124784 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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