AbstractIn this work three implicit methods are considered for the solution of the constant‐coefficient diffusion‐convection equation. Two of these methods are seen to be first and second‐order accurate in time and to be L‐stable or L0‐stable, depending on the relation between the convection and diffusion parameters and the step size. The third one is seen to be third‐order accurate in time and is also L‐stable (L0‐stable). However, some oscillations may appear in the solution. To avoid these oscillations some restriction