A finite difference solution of the regularized long-wave equation

Mathematical Problems in Engineering (Impact Factor: 1.38). 01/2006; DOI:10.1155/MPE/2006/85743
Source: DOAJ

ABSTRACT A linearized implicit finite difference method to obtain numerical solution of the one-dimensional regularized long-wave (RLW) equation is presented. The performance and the accuracy of the method are illustrated by solving three test examples of the problem: a single solitary wave, two positive solitary waves interaction, and an undular bore. The obtained results are presented and compared with earlier work.

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    ABSTRACT: In this work, our main purpose is to develop of a sufficiently robust, accurate and efficient numerical scheme for the solution of the regularized long wave (RLW) equation, an important partial differential equation with quadratic nonlinearity, describing a large number of physical phenomena. The crucial idea is based on the discretization of the RLW equation with the aid of a combination of the discontinuous Galerkin method for the space semi-discretization and the backward difference formula for the time discretization. Furthermore, a suitable linearization preserves a linear algebraic problem at each time level. We present error analysis of the proposed scheme for the case of nonsymmetric discretization of the dispersive term. The appended numerical experiments confirm theoretical results and investigate the conservative properties of the RLW equation related to mass, momentum and energy. Both procedures illustrate the potency of the scheme consequently. PACS Codes: 02.70.Dh, 02.60 Cb, 02.60.Lj, 03.65.Pm, 02.30.-f. MSC: 65M60, 65M15, 65M12, 65L06, 35Q53.
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