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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 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...
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