Abstract
AbstractA numerical simulation of the regularized long wave (RLW) equation is obtained using a high‐order compact difference method, based on the fourth‐order compact difference scheme in space and the fourth‐order Runge–Kutta method in time integration. The method is tested on the problems of propagation of a solitary wave, interaction of two positive solitary waves, interaction of a positive and a negative solitary wave, the evaluation of Maxwellian pulse into stable solitary waves, the development of an undular bore and the solitary waves induced by boundary motion. The three invariants of the motion are calculated to determine the conservation properties of the algorithm. L2 and L∞ error norms are used to measure differences between the exact and numerical solutions. The results obtained by proposed method are compared with those of other recently published methods and shown to be more accurate and efficient. Copyright © 2006 John Wiley & Sons, Ltd.
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