Stability analysis of six-point finite difference schemes for the constant coefficient convective-diffusion equation

AbstractA comprehensive and systematic study is presented to derive stability properties of various two-level, six-point finite difference schemes (in particular, difference schemes of Padé type) for the approximation to the constant coefficient convective-diffusion equation. First, the modified equivalent partial differential equation (MEPDE) for a general six-point difference scheme is derive. The MEPDE provides direct information on the order of accuracy of a difference scheme. The von Neumann and matrix methods are then employed to deduce the necessary and sufficient conditions for the numerical stability for the six-point difference schemes. An unified technique is developed to find the stability regions for the difference schemes. Some new second and third order six-point difference schemes for the approximation of the constant coefficient convective-diffusion equation are presented