Generalized BDF (Backward Differentiation Formula) Methods Applied to Hessenberg Form DAEs (Differential Algebraic Equations).

摘要

We study the numerical solution of Hessenberg form differential algebraic equations by variable stepsize generalized backward difference formulae (GBDF). GBDF methods of sufficiently high order are shown to converge for problems of index two, three, or four. The proof techniques developed are not sufficiently powerful to show convergence for index five problems. In addition we perform very high precision numerical experiments on problems of index two, three, four, and five using the standard six step backward difference formula. The experiments confirm the analysis regarding the error behavior of the index two and three problems, but suggest that the analysis of the index four problem is too pessimistic. It appears from the experiments that index five problems can also be solved by GBDF methods. 12 refs., 99 figs., 12 tabs.