Stability analysis of six-point finite difference schemes for the constant coefficient convective-diffusion equation (Q1205880)

The author studies the approximation and stability properties of two level, six-point finite difference schemes \[ a_ 1 T_{j+1}^{n+1}+a_ 0 T_ j^{n+1}a_{-1}T^{n+1}_{j-1}=b_ 1 T_{j+1}^ n +b_ 0 T_ j^ n+b_{-1} T_{j-1}^ n \] for the constant coefficient convection-diffusion equation \(\partial T/\partial t+u(\partial T/\partial x)=\gamma(\partial^ 2 T/\partial x^ 2)\), \(0<x<L\), \(t>0\), with the initial condition \(T(x,0)=f(x)\) and the Dirichlet boundary conditions \(T(0,t)=g_ 1(t)\) and \(T(L,t)=g_ 2(t)\). He derives some stable second and third order six-point finite difference schemes.