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A \(B\)-spline finite element method for the regularized long wave equation. (English) Zbl 0819.65125

For the solution of the equation \(u_ t + u_ x + auu_ x + bu_{xxt} = 0\) the authors consider a Galerkin method with quadratic \(B\)-splines, applying Crank-Nicolson for time stepping. (The solution of the nonlinearity is not mentioned.) The method is reported to be linearly stable. An exact solitary wave solution is used to test the accuracy of the approach; finally, it is applied to the simulation of an undular bore. Here too, no stability problems were experienced.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L75 Higher-order nonlinear hyperbolic equations
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References:

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