Three-level average linear difference scheme for the general improved KdV equation

Abstract:

In this paper, a numerical method for an initial-boundary value problem of the general Improved KdV equation is considered. A three-level average linear-implicit finite difference scheme is proposed and the existence and uniqueness are discussed. It is shown that the finite difference scheme is of second-order convergence and unconditionally stable. Numerical experiments verify the theoretical results.

Key words:GIKdV equation, linear difference scheme, convergence, stability