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Zbl 0717.65072
Gardner, L.R.T.; Gardner, G.A.
Solitary waves of the regularised long-wave equation. (English)
[J] J. Comput. Phys. 91, No.2, 441-459 (1990). ISSN 0021-9991

Authors' summary: A finite element solution of the regularized long wave equation, based on Galerkin's method using cubic splines as element shape functions, is set up. A linear stability analysis shows the scheme to be unconditionally stable. Test problems, including the migration 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. The temporal evolution of a Maxwellian initial pulse is then studied.
[W.Ames]

MSC 2000:: *65M60 Finite numerical methods (IVP of PDE)
65M12 Stability and convergence of numerical methods (IVP of PDE)
35Q53 KdV-like equations
35L70 Second order nonlinear hyperbolic equations

Keywords: unconditional stability; finite element; regularized long wave equation; Galerkin's method; cubic splines; linear stability; Test problems; solitary waves; Maxwellian initial pulse

Cited in: Zbl 0759.65086

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Zentralblatt MATH Berlin [Germany]