IJPAM: Volume 108, No. 1 (2016)

HAAR WAVELETS BASED TIME DISCRETIZATION
TECHNIQUE FOR SOLVING NONLINEAR PARTIAL
DIFFERENTIAL EQUATIONS

Harpreet Kaur$^1$, Shin Min Kang$^2$
$^{1}$Department of Mathematics
School of Physical Sciences
Lovely Professional University
Phagwara, 144411, Punjab, INDIA
$^{2}$Department of Mathematics and RINS
Gyeongsang National University
Jinju 52828, KOREA


Abstract. A new numerical technique is developed to find the solutions of general nonlinear partial differential equations. The technique is based on the time discretization of Haar wavelet series approximations with quasilinearization process. In order to test the efficiency of the proposed technique, it is applied on well known nonlinear partial differential equations such as the generalized regularized long wave equation, the Benjamin Bona-Mahony equation and the Fitzhugh-Nagumo equation. Numerical results are obtained by preparing MATLAB codes of proposed techniques. The beautiful concentration profiles of $u$ and $v$ are shown by figures at different time level and error norms $L_2$ and $L_\infty$ are calculated.

Received: March 9, 2016

AMS Subject Classification: 35Qxx, 41A65, 65Nxx, 65T60

Key Words and Phrases: Haar wavelet, operational matrix, nonlinear partial differential equation, quasilinearization process, time discretization of Haar wavelet series

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DOI: 10.12732/ijpam.v108i1.8 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 108
Issue: 1
Pages: 63 - 78


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