The line method with high order accuracy for a kind of one dimension convection_diffusion equations is presented by discretizing locally partial differential equations (PDE), which is based on the high order accurate solver-SEV ORD for ordinary differential equations (ODE) with boundary value problems. By using local one dimension method, the alternate direction line algorithm with high order accuracy is given for two dimension convection_diffusion problems.

A two point scheme with high order accuracy on arbitrary mesh is presented for a kind of singular perturbation problems based on the idea of[1].Some improvements about boundary treatment and keeping stability are also given.Numerical examples found the method more convenient and efficient for singular perturbation problems.