Title

A Numerical Method For A Nonlocal Elliptic Boundary Value Problem

Abstract

In 2005 Corrêa and Filho established existence and uniqueness results for the nonlinear PDE: -δu = g(x,u)α; ∫Ω f(x,u) β;, which arises in physical models of thermodynamical equilibrium via Coulomb potential, among others [3]. In this work we discuss a numerical method for a special case of this equation: -α(∫10 u(t)dt u" = f(x), 0 < x < 1, u(0) = a, u(1) = b. We first consider the existence and uniqueness of the analytic problem using a fixed point argument and the contraction mapping theorem. Next, we evaluate the solution of the numerical problem via a finite difference scheme. From there, the existence and convergence of the approximate solution will be addressed as well as a uniqueness argument, which requires some additional restrictions. Finally, we conclude the work with some numerical examples where an interval-halving technique was implemented. © 2008 Rocky Mountain Mathematics Consortium.

Publication Date

12-1-2008

Publication Title

Journal of Integral Equations and Applications

Volume

20

Issue

2

Number of Pages

243-261

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1216/JIE-2008-20-2-243

Socpus ID

67349275441 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/67349275441

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