Numerical study of a conservative weighted compact difference scheme for the symmetric regularized long wave equations. (English) Zbl 1416.76185
Summary: In this article, a new weighted and compact conservative difference scheme for the symmetric regularized long wave (SRLW) equations is considered. The new scheme is decoupled and linearized in practical computation, that is, at each time step only two tridiagonal systems of linear algebraic equations need to be solved. It is proved by the discrete energy method that the compact scheme is uniquely solvable, the convergence and stability of the difference scheme are obtained, and its numerical convergence order is \(O(\tau^2+h^4)\) in the \(L^\infty\)-norm. Numerical experiment results show that the scheme is efficient and reliable.
MSC:
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 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 |
| 65M25 | Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs |
| 35Q35 | PDEs in connection with fluid mechanics |
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
Keywords:
compact difference scheme; conservative; convergence in \(L^\infty\)-norm; SRLW equations; stabilityReferences:
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