Abstract: 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.

Key words: prominent convection, local one dimension method, high order accuracy, line method