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2014 An Efficient Collocation Method for a Class of Boundary Value Problems Arising in Mathematical Physics and Geometry
A. H. Bhrawy, A. S. Alofi, R. A. Van Gorder
Abstr. Appl. Anal. 2014(SI40): 1-9 (2014). DOI: 10.1155/2014/425648

Abstract

We present a numerical method for a class of boundary value problems on the unit interval which feature a type of power-law 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 ( α , β ) ( r ) with α , β ( - 1 , ) , r ( 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.

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A. H. Bhrawy. A. S. Alofi. R. A. Van Gorder. "An Efficient Collocation Method for a Class of Boundary Value Problems Arising in Mathematical Physics and Geometry." Abstr. Appl. Anal. 2014 (SI40) 1 - 9, 2014. https://doi.org/10.1155/2014/425648

Information

Published: 2014
First available in Project Euclid: 6 October 2014

zbMATH: 07022369
MathSciNet: MR3212426
Digital Object Identifier: 10.1155/2014/425648

Rights: Copyright © 2014 Hindawi

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Vol.2014 • No. SI40 • 2014
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