Numerical computation of nonlinear fractional Zakharov–Kuznetsov equation arising in ion-acoustic waves

Document Type : Original Article

Authors

1 Department of Mathematics, Jagan Nath Gupta Institute of Engineering and Technology, Jaipur 302022, Rajasthan, India

2 Department of Mathematics, Jagan Nath University, Village-Rampura, Tehsil-Chaksu, Jaipur 303901, Rajasthan, India

3 Department of Mathematics, National Institute of Technology, Jamshedpur 831014, Jharkhand, India

Abstract

The main aim of the present work is to propose a new and simple algorithm for fractional
Zakharov–Kuznetsov equations by using homotopy perturbation transform method (HPTM). The Zakharov–Kuznetsov equation was first derived for describing weakly nonlinear ion-acoustic waves in strongly magnetized lossless plasma in two dimensions. The homotopy perturbation transform method is an innovative adjustment in Laplace transform algorithm (LTA) and makes the calculation much simpler. HPTM is not limited to the small parameter, such as in the classical perturbation method. The method gives an analytical solution in the form of a convergent
series with easily computable components, requiring no linearization or small perturbation.
The numerical solutions obtained by the proposed method indicate that the approach is easy to
implement and computationally very attractive.

Keywords

Journal of the Egyptian Mathematical Society
Volume 22, Issue 3 - Serial Number 3
October 2014
Pages 373-378

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