Avoiding stability-induced inefficiencies in BDF methods (Q913463)

The backward differentiation formulas (BDF) are often dismissed in the numerical solution of ODEs, especially ODEs arising from semidiscretization of time-dependent PDEs. This is due to their poor stability behaviour near the imaginary axis for orders three and above. The author examines the behaviour in details and explains why and for what problems this happens, what the appropriate tactic should be, and why this is not the tactic in most traditional automatic codes. She presents an idea avoiding this inefficiency.