Title

On a numerical method for a homogeneous, nonlinear, nonlocal, elliptic boundary value problem

Authors

Authors

J. R. Cannon;D. J. Galiffa

Comments

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Abbreviated Journal Title

Nonlinear Anal.-Theory Methods Appl.

Keywords

Numerical method; Nonlocal; Elliptic; Boundary value problem; Fixed; point; Mapping; POSITIVE SOLUTIONS; Mathematics, Applied; Mathematics

Abstract

In this work we develop a numerical method for the equation: -alpha (integral(1)(0) u(t)dt) u ''(x) + [u(x)](2n+1) = 0, x is an element of (0, 1), u(0) = a, u(1) = b. We begin by establishing a priori estimates and the existence and uniqueness of the solution to the nonlinear auxiliary problem via the Schauder fixed point theorem. From this analysis, we then prove the existence and uniqueness to the problem above by defining a continuous compact mapping, utilizing the a priori estimates and the Brouwer fixed point theorem. Next, we analyze a discretization of the above problem and show that a solution to the nonlinear difference problem exists and is unique and that the numerical procedure converges with error O(h). We conclude with some examples of the numerical process. Published by Elsevier Ltd

Journal Title

Nonlinear Analysis-Theory Methods & Applications

Volume

74

Issue/Number

5

Publication Date

1-1-2011

Document Type

Article

Language

English

First Page

1702

Last Page

1713

WOS Identifier

WOS:000286178200017

ISSN

0362-546X

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