• NUMERICAL SOLUTION OF THE FRACTIONAL KORTEWEG–DE VRIES (KdV) EQUATION BY q-HOMOTOPY ANALYSIS METHOD (q-HAM)

Dr. ANOOP KUMAR*

Abstract


In this paper, we consider the fractional Korteweg–de Vries (KdV) equation. A relatively new method called the q-homotopy analysis method (q-HAM) is adopted to obtain an analytical solution of the fractional Korteweg–de Vries (KdV) equation in series form. Our analysis shows the simplicity nature of the application of q-HAM to nonlinear fractional differential equations. The convergence rate of the method used is faster in the sense that just very few terms of the series solution are needed for a good approximation due to the presence of the auxiliary parameter h comparable to exact solutions. Numerical solution obtained by this method is compared with the exact solution. Our error analysis shows that the analytical solution converges very rapidly to the exact solution. Numerical results are obtained using the software Mathematica.


Keywords


q-homotopy analysis method (q-HAM), fractional Korteweg–de Vries (KdV) equation, approximate numerical solutions, symbolic computation.

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