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
ISSN
1085-3375
Recommended Citation
Bhrawy, A. H.; Alofi, A. S.; and Van Gorder, R. A., "An Efficient Collocation Method for a Class of Boundary Value Problems Arising in Mathematical Physics and Geometry" (2014). Faculty Bibliography 2010s. 5075.
https://stars.library.ucf.edu/facultybib2010/5075
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