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An efficient computational approach for generalized Hirota-Satsuma coupled KdV equations arising in shallow water waves

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Gupta S., Kumar D., Singh J.

Waves, Wavelets and Fractals

2017

tom 3

nr 1

14-30

The aim of this letter is to present a numerical algorithm for generalized Hirota-Satsuma coupled KdV equations arising in unidirectional propagation of shallow water waves by using the homotopy analysis transform technique. The computational approach is the merged form of the homotopy analysis technique and Laplace transform scheme. The technique provides a series solution, which converges very fast, components are very easily calculated, and it does not require linearization or small perturbation. The numerical and graphical results derived by making use of proposed approach indicate that the scheme is very user friendly and easy to implement.

An efficient computational approach for linear and nonlinear fractional differential equations

100%

Singh J., Kumar D., Swroop R., Sharma R. P.

Waves, Wavelets and Fractals

2017

tom 3

nr 1

1-13

The pivotal aim of this article is to propose an efficient computational technique namely q-homotopy analysis transform method (q-HATM) to solve the linear and nonlinear time-fractional partial differential equation. In q-HATM iterative process, we investigate the behavior of independent variable for convergent series solution in admissible range. The q-HATM technique manipulates and controls the series solution, which rapidly converges to the exact solution in large admissible domain in a very efficient way. The solution procedure and explanation show the flexible efficiency of q-HATM, compared to other existing classical techniques for solving three different kind of time-fractional partial differential equations.

Ograniczanie wyników

2 Waves, Wavelets and Fractals

2 Kumar D.

2 Singh J.

1 Gupta S.

1 Sharma R. P.

1 Swroop R.

2 2017

Wyniki wyszukiwania

An efficient computational approach for generalized Hirota-Satsuma coupled KdV equations arising in shallow water waves

An efficient computational approach for linear and nonlinear fractional differential equations