Abstract
New modified Adomian decomposition method is proposed for the solution of the generalized fifth-order Korteweg-de Vries (GFKdV) equation. The numerical solutions are compared with the standard Adomian decomposition method and the exact solutions. The results are demonstrated which confirm the efficiency and applicability of the method.
Highlights
The fifth-order KdV is the essential a model foe several physical phenomena including shallow-water waves near critical value of surface tension and waves in nonlinear LC circuit with mutual inductance between neighbouring inductors [1]
New modified Adomian decomposition method is proposed for the solution of the generalized fifth-order Korteweg-de Vries (GFKdV) equation
The numerical solutions are compared with the standard Adomian decomposition method and the exact solutions
Summary
The fifth-order (or generalized) KdV is the essential a model foe several physical phenomena including shallow-water waves near critical value of surface tension and waves in nonlinear LC circuit with mutual inductance between neighbouring inductors [1]. Djidjeli et al proposed finite deference schemes based on a predictor corrector algorithm and a linearized implicit method for the third and fifth order KdV equations. Some of these methods are not easy to use and sometimes require tedious work and calculation [7, 8]. Kaya calculated the explicit and numerical solutions of some fifth-order KdV equation by decomposition method and Kaya and El-Sayed in [14] proved the convergence of (ADM) applied to (gfKdV) equation. Wazwaz [16] presented a reliable modification of the Adomian decomposition method. We generalized an appropriate Adomian’s polynomials for (gfKdV) equation will be handle more quickly, and elegantly by implementing the new modified (ADM) rather than traditional methods for the exact solution of which is to be obtained subject to initial condition
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