Finite-Difference Method for Solving the One-Dimensional Convection-Diffusion Equation with Second Order of Accuracy

Implicit difference scheme with second order of accuracy is constructed for convection - diffusion equation ∂ u/∂ t + c ∂ u/∂ x = μ ∂ ²u/∂ x² . The difference scheme turns into Crank - Nicolson difference scheme if c=0. If μ = 0 the difference scheme turns into implicit difference scheme that is very alike Lax - Wendroff difference scheme. Numerical comparison of the difference scheme with other difference schemes for convection - diffusion equation was fulfilled. Property of monotony of solution conserving of the difference scheme was investigated.