Hybrid difference scheme is a method used in the numerical solution for convection-diffusion problems. These problems play important roles in computational fluid dynamics. It can be described by the general partial equation as follows:
Where,  is density,  is the velocity vector,  is the diffusion coefficient and  is the source term. In this equation property,  can be temperature, internal energy or component of velocity vector  in x, y and z directions.
For one-dimensional analysis of convection-diffusion problem in steady state and without the source the equation reduces to,
With boundary conditions,  and , where L is the length,  and  are the given values.