An Efficient Collocation Method for a Class of Boundary Value Problems Arising in Mathematical Physics and Geometry
Joint Authors
Bhrawy, Ali H.
Van Gorder, Robert A.
Alofi, Abdulaziz
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-05-15
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Bhrawy, Ali H.& Alofi, Abdulaziz& Van Gorder, Robert A.. 2014. An Efficient Collocation Method for a Class of Boundary Value Problems Arising in Mathematical Physics and Geometry. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-1013913
Modern Language Association (MLA)
Bhrawy, Ali H.…[et al.]. An Efficient Collocation Method for a Class of Boundary Value Problems Arising in Mathematical Physics and Geometry. Abstract and Applied Analysis No. 2014 (2014), pp.1-9.
https://search.emarefa.net/detail/BIM-1013913
American Medical Association (AMA)
Bhrawy, Ali H.& Alofi, Abdulaziz& Van Gorder, Robert A.. An Efficient Collocation Method for a Class of Boundary Value Problems Arising in Mathematical Physics and Geometry. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-1013913
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1013913