AbstractA family of methods is developed for the numerical solution of second‐order parabolic partial differential equations in one space dimension. The methods are second‐, third‐, or fourth‐order accurate in time; five of them are seen to beL0‐stable in the sense of Gourlay and Morris, while the sixth is seen to beA0‐stable, The methods are tested on four problems from the literature, three diffusion problems and one reaction–diff