A numerical study of the long wave–short wave interaction equations

H. Borluk, G.M. Muslu and H.A. Erbay

Mathematics and Computers in Simulation (MATCOM), 2007, vol. 74, issue 2, 113-125

Abstract: Two numerical methods are presented for the periodic initial-value problem of the long wave–short wave interaction equations describing the interaction between one long longitudinal wave and two short transverse waves propagating in a generalized elastic medium. The first one is the relaxation method, which is implicit with second-order accuracy in both space and time. The second one is the split-step Fourier method, which is of spectral-order accuracy in space. We consider the first-, second- and fourth-order versions of the split-step method, which are first-, second- and fourth-order accurate in time, respectively. The present split-step method profits from the existence of a simple analytical solution for the nonlinear subproblem. We numerically test both the relaxation method and the split-step schemes for a problem concerning the motion of a single solitary wave. We compare the accuracies of the split-step schemes with that of the relaxation method. Assessments of the efficiency of the schemes show that the fourth-order split-step Fourier scheme is the most efficient among the numerical schemes considered.

Keywords: Relaxation method; Split-step method; Long wave–short wave interaction equations; Solitary waves (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:74:y:2007:i:2:p:113-125

DOI: 10.1016/j.matcom.2006.10.016

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