A single cell high order scheme for the convection‐diffusion equation with variable coefficients

Abstract A new finite difference scheme for the convection‐diffusion equation with variable coefficients is proposed. The difference scheme is defined on a single square cell of size 2 h over a 9‐point stencil and has a truncation error of order h 4 . The resulting system of equations can be solved by iterative methods. Numerical results of some test problems are given.