We develop a general framework for designing conservative numerical methods based on
summation by parts operators and split forms in space, combined with relaxation Runge …

This paper proposes a new, conservative fully discrete scheme for the numerical solution of
the regularized shallow water Boussinesq system of equations in the cases of periodic and …

In this paper, we study the Symmetric Regularized Long Wave (SRLW) equations by finite
difference method. We design some numerical schemes which preserve the original …

An extensive assessment of the accuracy of explicit finite difference methods for the solution
of the equal-width (EW) and regularized long-wave (RLW) equations is reported. Such an …

The purpose of this paper is to show the advantages that represent the use of numerical
methods that preserve invariant quantities in the study of solitary wave interactions for the …

We consider entropy conservative and dissipative discretizations of nonlinear conservation
laws with implicit time discretizations and investigate the influence of iterative methods used …

We study the numerical error in solitary wave solutions of nonlinear dispersive wave
equations. A number of existing results for discretizations of solitary wave solutions of …

Coupled with the Richardson extrapolation, a new conservative Crank–Nicolson finite
difference scheme, which has the accuracy of O (τ 2+ h 4) without refined mesh for the …

In this paper, a decoupled finite difference scheme with fourth-order accuracy is proposed to
solve the Symmetric Regularized Long Wave equation. The scheme is proved to conserve …

In this paper we analyse the behaviour in time of the numerical approximations to solitary
wave solutions of the generalized Benjamin–Bona–Mahony equation. This equation …