An interesting global stabilisation of a locally short-range unstable high-order scheme for the digital simulation of the diffusion equation

The (5, 5)-point scheme of Kimble and White (1990) for discretising a parab olic partial differential equation is shown to be inherently (locally) unco nditionally unstable, as is the corresponding five-point scheme for solving an ordinary differential equation. However, by casting the time-marching p roblem into a large matrix equation and terminating the system with some as ymmetric backward differentiation (5, 5)-point discretisations, Kimble and White stabilised the system and achieved high-order accuracy using it. By r educing the number of points in time, the scheme could, in principle, be us ed to start a multi-level scheme such as BDF. (C) 1999 Elsevier Science Ltd . All rights reserved.