Title

An Efficient Collocation Method for a Class of Boundary Value Problems Arising in Mathematical Physics and Geometry

Authors

Authors

A. H. Bhrawy; A. S. Alofi;R. A. Van Gorder

Comments

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Abbreviated Journal Title

Abstract Appl. Anal.

Keywords

SPECTRAL-GALERKIN METHOD; NUMERICAL-SOLUTION; YAMABE-EQUATION; JACOBI

Abstract

We present a numerical method for a class of boundary value problems on the unit interval which feature a type of powerlaw nonlinearity. In order to numerically solve this type of nonlinear boundary value problems, we construct a kind of spectral collocation method. The spatial approximation is based on shifted Jacobi polynomials J(n)((alpha,beta))(r) with alpha,beta epsilon (-1, infinity), r epsilon (0,1) and n the polynomial degree. The shifted Jacobi-Gauss points are used as collocation nodes for the spectral method. After deriving the method for a rather general class of equations, we apply it to several specific examples. One natural example is a nonlinear boundary value problem related to the Yamabe problem which arises in mathematical physics and geometry. A number of specific numerical experiments demonstrate the accuracy and the efficiency of the spectral method. We discuss the extension of the method to account for more complicated forms of nonlinearity.

Journal Title

Abstract and Applied Analysis

Publication Date

1-1-2014

Document Type

Article

Language

English

First Page

9

WOS Identifier

WOS:000336362300001

ISSN

1085-3375

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