We apply the method of operator splitting on the generalized Korteweg--de Vries (KdV)
equation ut+ f (u) x+ ϵuxxx= 0, by solving the nonlinear conservation law ut+ f (u) x= 0 and …

In this paper we study the convergence of a centred finite difference scheme on a non-
uniform mesh for a 1D elliptic problem subject to general boundary conditions. On a non …

In this paper, we study the convergence of a finite difference scheme on nonuniform grids for
the solution of second-order elliptic equations with mixed derivatives and variable …

This paper deals with the supraconvergence of elliptic finite difference schemes on variable
grids for second order elliptic boundary value problems subject to Dirichlet boundary …

This paper is the second of a series in which a general theory of a priori error estimates for
scalar conservation laws is constructed. In this paper, we focus on how the lack of …

This paper is the third of a series in which a general theory of a priori error estimates for
scalar conservation laws is constructed. In this paper, we consider multidimensional flux …

In this paper we study the convergence properties of a cell-centered finite difference scheme
for second order elliptic equations with variable coefficients subject to Dirichlet boundary …

In this paper, we study the convergence of the finite difference discretization of a second
order elliptic equation with variable coefficients subject to general boundary conditions. We …

The present problem was first studied by Schneider, JFM 726 (2013). An asymptotic analysis
was performed for small slope of the plane channel bottom and slightly supercritical, fully …

In this paper we study the convergence properties of a finite difference discretization of a
second order elliptic equation with mixed derivatives and variable coefficient in polygonal …