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A computational method for the equal width equation. (English) Zbl 1047.65086
Summary: A B-spline finite element method is used to solve the equal width equation numerically. This approach involves a collocation method using quintic B-splines at the knot points as element shape. Time integration of the resulting system of ordinary differential equations is effected using the fourth-order Runge-Kutta method, instead of the finite difference method, the resulting system of ordinary differential equations is integrated with respect to time. Standard problems are used to validate the algorithm which is then used to model the smooth development of an undular bore.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
76B25 Solitary waves for incompressible inviscid fluids
35Q51 Soliton equations
65L12 Finite difference and finite volume methods for ordinary differential equations
76M10 Finite element methods applied to problems in fluid mechanics
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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References:
[1] DOI: 10.1016/S0045-7825(99)00312-6 · Zbl 0963.76057
[2] DOI: 10.1016/S0045-7825(99)00462-4 · Zbl 1011.76048
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