A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations
Joint Authors
Sibanda, Precious
Magagula, V. M.
Motsa, Sandile Sydney
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-08-26
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs).
The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation.
In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation.
The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method.
There is congruence between the numerical results and the exact solutions to a high order of accuracy.
Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
American Psychological Association (APA)
Motsa, Sandile Sydney& Magagula, V. M.& Sibanda, Precious. 2014. A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations. The Scientific World Journal،Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-1050192
Modern Language Association (MLA)
Motsa, Sandile Sydney…[et al.]. A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations. The Scientific World Journal No. 2014 (2014), pp.1-13.
https://search.emarefa.net/detail/BIM-1050192
American Medical Association (AMA)
Motsa, Sandile Sydney& Magagula, V. M.& Sibanda, Precious. A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations. The Scientific World Journal. 2014. Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-1050192
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1050192