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

Abstract and Applied Analysis

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

Mathematics

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