Numerical analysis of a linear-implicit average scheme for generalized Benjamin-Bona-Mahony-Burgers equation. (English) Zbl 1235.76090
Summary: A linear-implicit finite difference scheme is given for the initial-boundary problem of GBBM-Burgers equation, which is convergent and unconditionally stable. The unique solvability of numerical solutions is shown. A priori estimate and second-order convergence of the finite difference approximate solution are discussed using energy method. Numerical results demonstrate that the scheme is efficient and accurate.
MSC:
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
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