Numerical Analysis of the Coupled Fractional Whitham-Broer-Kaup System
Keywords:
Coupled modified Boussinesq and approximate long wave equations, homotopy analysis method, Shehu transform, Caputo fractional derivativeAbstract
In the current study, we derive the analytical solution of applications of Coupled modified Boussinesq and approximate long wave equations, a significant mathematical model for representing wave propagation in shallow water. The solution is obtained through the utilization of the q-homotopy analysis Shehu transform method (q-HASTM), a hybrid approach combining Shehu transformation and the q-homotopy analysis method. Homotopy polynomials are employed to address non-linear terms, and the introduced algorithm incorporates the auxiliary parameter $\hbar$ and $n$ to regulate the convergence region of the resulting series solution. Comparative numerical analyses are conducted with outcomes from the Adomian decomposition method (ADM), variational iteration method (VIM), optimal homotopy asymptotic method (OHAM) and residue power series method (RPSM), demonstrating the superior accuracy of the proposed method. The method's novelty and straightforward implementation establish it as a reliable and efficient analytical technique for solving both linear and non-linear fractional partial differential equations.
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