On the convergence of difference schemes for the generalized BBM–Burgers equation

Abstract

Abstract A three-level finite difference scheme is studied for the initial-boundary value problem of the generalized Benjamin–Bona–Mahony–Burgers equation. The obtained algebraic equations are linear with respect to the values of the desired function for each new level. The unique solvability and absolute stability of the difference scheme are shown. It is proved that the scheme is convergent with the rate of order k - 1 {k-1} when the exact solution belongs to the Sobolev space W 2 k ⁢ ( Q ) {W_{2}^{k}(Q)} , 1 < k ≤ 3 {1<k\leq 3} .