Multigrid Solution of an Elliptic Fredholm Partial Integro-Differential Equation with a Hilbert-Schmidt Integral Operator

Author: Duncan Kioi Gathungu, Alfio Borzì

ABSTRACT
An efficient multigrid finite-differences scheme for solving elliptic Fredholm partial integro-differential equations (PIDE) is discussed. This scheme combines a second-order accurate finite difference discretization of the PIDE problem with a multigrid scheme that includes a fast multilevel integration of the Fredholm operator allowing the fast solution of the PIDE problem. Theoretical estimates of second-order accuracy and results of local Fourier analysis of convergence of the proposed multigrid scheme are presented. Results of numerical experiments validate these estimates and demonstrate optimal computational complexity of the proposed framework.

Source:

Journal: Applied Mathematics


DOI: 10.4236/am.2017.87076 (PDF)
Paper Id: 77695 (metadata)

See also: Comments to Paper

About scirp

(SCIRP: http://www.scirp.org) is an academic publisher of open access journals. It also publishes academic books and conference proceedings. SCIRP currently has more than 200 open access journals in the areas of science, technology and medicine. Readers can download papers for free and enjoy reuse rights based on a Creative Commons license. Authors hold copyright with no restrictions. SCIRP calculates different metrics on article and journal level. Citations of published papers are shown based on Google Scholar and CrossRef. Most of our journals have been indexed by several world class databases. All papers are archived by PORTICO to guarantee their availability for centuries to come.
This entry was posted in AM. Bookmark the permalink.

Leave a Reply

Your email address will not be published. Required fields are marked *