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A linearized implicit pseudo-spectral method for some model equations: the regularized long wave equations

A linearized implicit pseudo-spectral method for some model equations: the regularized long wave equations
A linearized implicit pseudo-spectral method for some model equations: the regularized long wave equations
An efficient numerical method is developed for the numerical solution of non-linear wave equations typified by the regularized long wave equation (RLW) and its generalization (GRLW). The method developed uses a pseudo-spectral (Fourier transform) treatment of the space dependence together with a linearized implicit scheme in time. An important advantage to be gained from the use of this method, is the ability to vary the mesh length, thereby reducing the computational time. Using a linearized stability analysis, it is shown that the proposed method is unconditionally stable. The method is second order in time and all-order in space. The method presented here is for the RLW equation and its generalized form, but it can be implemented to a broad class of non-linear long wave equations, with obvious changes in the various formulae. Test problems, including the simulation of a single soliton and interaction of solitary waves, are used to validate the method, which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.
regularized long waves (rlw), solitary and periodic wave solutions, homoclinic and periodic orbits, pseudo-spectral, linearized implicit method, unconditional stability
1069-8299
847-863
Djidjeli, K.
94ac4002-4170-495b-a443-74fde3b92998
Price, W.G.
b7888f47-e3fc-46f4-9fb9-7839052ff17c
Twizell, E.H.
46b3dc67-c9d6-414d-a8cf-19c0c0911935
Cao, Q.
f1f67041-4813-43e7-94ce-ff9052f60443
Djidjeli, K.
94ac4002-4170-495b-a443-74fde3b92998
Price, W.G.
b7888f47-e3fc-46f4-9fb9-7839052ff17c
Twizell, E.H.
46b3dc67-c9d6-414d-a8cf-19c0c0911935
Cao, Q.
f1f67041-4813-43e7-94ce-ff9052f60443

Djidjeli, K., Price, W.G., Twizell, E.H. and Cao, Q. (2003) A linearized implicit pseudo-spectral method for some model equations: the regularized long wave equations. Communications in Numerical Methods in Engineering, 19 (11), 847-863. (doi:10.1002/cnm.635).

Record type: Article

Abstract

An efficient numerical method is developed for the numerical solution of non-linear wave equations typified by the regularized long wave equation (RLW) and its generalization (GRLW). The method developed uses a pseudo-spectral (Fourier transform) treatment of the space dependence together with a linearized implicit scheme in time. An important advantage to be gained from the use of this method, is the ability to vary the mesh length, thereby reducing the computational time. Using a linearized stability analysis, it is shown that the proposed method is unconditionally stable. The method is second order in time and all-order in space. The method presented here is for the RLW equation and its generalized form, but it can be implemented to a broad class of non-linear long wave equations, with obvious changes in the various formulae. Test problems, including the simulation of a single soliton and interaction of solitary waves, are used to validate the method, which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.

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Published date: 2003
Keywords: regularized long waves (rlw), solitary and periodic wave solutions, homoclinic and periodic orbits, pseudo-spectral, linearized implicit method, unconditional stability

Identifiers

Local EPrints ID: 22237
URI: https://eprints.soton.ac.uk/id/eprint/22237
ISSN: 1069-8299
PURE UUID: 43e7d665-cd0d-4b63-91c7-46dc9ce194dc

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Date deposited: 17 Mar 2006
Last modified: 17 Jul 2017 16:23

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