Abstract:

In the present study, the meshless method based on radial basis functions is applied for finding the numerical solution of the general Rosenau KdV-RLW equation. Firstly, Crank-Nicolson and forward finite difference methods are used for discretization of the unknown function  and its time derivative, respectively. A linearization technique is applied for the approximate solution of the equation. Secondly, we calculate the numerical values of invariants of the motions to examine the fundamental conservative properties of the equation. Also, the error norms are computed to determine the accuracy of the proposed method. Linear stability analysis is tested to determine whether the present method is stable or unstable. The scheme gives unconditionally stable. At the end of this paper, obtained results indicate the accuracy and applicability of this method.

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