Improved exponential discretization method for convection-diffusion equation (Q1902261)

One-dimensional convection-diffusion parabolic equation \({\partial u\over \partial t}={\partial\over \partial x}\left( a{\partial u\over \partial x}\right) - b {\partial u\over \partial x}\) is discretized by grid equations on the basis of the known approach that requires that \(u=\text{const}\) and \(u=x-bt\) must be solutions of the discretized equations. Numerical examples given in the paper confirm the importance of such requirements.