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

    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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