Approximate Solution of Nonlinear Klein-Gordon Equation Using Sobolev Gradients
Joint Authors
Butt, Asma Rashid
Javid, Ahmad
Raza, Nauman
Source
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-03-02
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
The nonlinear Klein-Gordon equation (KGE) models many nonlinear phenomena.
In this paper, we propose a scheme for numerical approximation of solutions of the one-dimensional nonlinear KGE.
A common approach to find a solution of a nonlinear system is to first linearize the equations by successive substitution or the Newton iteration method and then solve a linear least squares problem.
Here, we show that it can be advantageous to form a sum of squared residuals of the nonlinear problem and then find a zero of the gradient.
Our scheme is based on the Sobolev gradient method for solving a nonlinear least square problem directly.
The numerical results are compared with Lattice Boltzmann Method (LBM).
The L2, L∞, and Root-Mean-Square (RMS) values indicate better accuracy of the proposed method with less computational effort.
American Psychological Association (APA)
Raza, Nauman& Butt, Asma Rashid& Javid, Ahmad. 2016. Approximate Solution of Nonlinear Klein-Gordon Equation Using Sobolev Gradients. Journal of Function Spaces،Vol. 2016, no. 2016, pp.1-7.
https://search.emarefa.net/detail/BIM-1108561
Modern Language Association (MLA)
Raza, Nauman…[et al.]. Approximate Solution of Nonlinear Klein-Gordon Equation Using Sobolev Gradients. Journal of Function Spaces No. 2016 (2016), pp.1-7.
https://search.emarefa.net/detail/BIM-1108561
American Medical Association (AMA)
Raza, Nauman& Butt, Asma Rashid& Javid, Ahmad. Approximate Solution of Nonlinear Klein-Gordon Equation Using Sobolev Gradients. Journal of Function Spaces. 2016. Vol. 2016, no. 2016, pp.1-7.
https://search.emarefa.net/detail/BIM-1108561
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1108561