Fast Spectral Collocation Method for Solving Nonlinear Time-Delayed Burgers-Type Equations with Positive Power Terms
Joint Authors
Assas, L. M.
Bhrawy, Ali H.
Alghamdi, Mohammad Ali
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-08-06
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
Since the collocation method approximates ordinary differential equations, partial differential equations, and integral equations in physical space, it is very easy to implement and adapt to various problems, including variable coefficient and nonlinear differential equations.
In this paper, we derive a Jacobi-Gauss-Lobatto collocation method (J-GL-C) to solve numerically nonlinear time-delayed Burgers-type equations.
The proposed technique is implemented in two successive steps.
In the first one, we apply (N-1) nodes of the Jacobi-Gauss-Lobatto quadrature which depend upon the two general parameters (θ,ϑ>-1), and the resulting equations together with the two-point boundary conditions constitute a system of (N-1) ordinary differential equations (ODEs) in time.
In the second step, the implicit Runge-Kutta method of fourth order is applied to solve a system of (N-1) ODEs of second order in time.
We present numerical results which illustrate the accuracy and flexibility of these algorithms.
American Psychological Association (APA)
Bhrawy, Ali H.& Assas, L. M.& Alghamdi, Mohammad Ali. 2013. Fast Spectral Collocation Method for Solving Nonlinear Time-Delayed Burgers-Type Equations with Positive Power Terms. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-495015
Modern Language Association (MLA)
Bhrawy, Ali H.…[et al.]. Fast Spectral Collocation Method for Solving Nonlinear Time-Delayed Burgers-Type Equations with Positive Power Terms. Abstract and Applied Analysis No. 2013 (2013), pp.1-12.
https://search.emarefa.net/detail/BIM-495015
American Medical Association (AMA)
Bhrawy, Ali H.& Assas, L. M.& Alghamdi, Mohammad Ali. Fast Spectral Collocation Method for Solving Nonlinear Time-Delayed Burgers-Type Equations with Positive Power Terms. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-495015
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-495015