Title

On A Numerical Method For A Homogeneous, Nonlinear, Nonlocal, Elliptic Boundary Value Problem

Keywords

Boundary value problem; Elliptic; Fixed point; Mapping; Nonlocal; Numerical method

Abstract

In this work we develop a numerical method for the equation: -α(∫01u(t)dt)u″(x)+[u(x)]2n+1=0,x∈(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 (h). We conclude with some examples of the numerical process. © 2010 Elsevier Ltd. All rights reserved.

Publication Date

3-1-2011

Publication Title

Nonlinear Analysis, Theory, Methods and Applications

Volume

74

Issue

5

Number of Pages

1702-1713

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.na.2010.10.042

Socpus ID

78651379279 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/78651379279

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