Numerical computation of nonlinear fractional Zakharov–Kuznetsov equation arising in ion-acoustic waves | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 22, Issue 3, October 2014, Pages 373-378 PDF (1.44 M) | ||
| Document Type: Original Article | ||
| Authors | ||
| Devendra Kumar1; Jagdev Singh2; Sunil Kumar3 | ||
| 1Department of Mathematics, Jagan Nath Gupta Institute of Engineering and Technology, Jaipur 302022, Rajasthan, India | ||
| 2Department of Mathematics, Jagan Nath University, Village-Rampura, Tehsil-Chaksu, Jaipur 303901, Rajasthan, India | ||
| 3Department 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 | ||
| Fractional Zakharov–Kuznetsov equations; Laplace transform; Homotopy perturbation transform method; He’s polynomials | ||
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