Modified extended backward differentiation formulae for the numerical solution of stiff initial value problems in ODEs and DAEs

For many years the methods of choice for the numerical solution of stiff initial value problems and certain classes of differential algebraic equations have been the well-known backward differentiation formulae (BDF). More recently, however, new classes of formulae which can offer some important adv...

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Bibliographic Details
Published in:	Journal of computational and applied mathematics Vol. 125; no. 1; pp. 117 - 130
Main Author:	Cash, J.R.
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 15.12.2000
Subjects:	Differential algebraic equations MEBDF Stiff differential equations Stiff differential equations MEBDF Differential algebraic equations
ISSN:	0377-0427, 1879-1778
Online Access:	Get full text
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Summary:	For many years the methods of choice for the numerical solution of stiff initial value problems and certain classes of differential algebraic equations have been the well-known backward differentiation formulae (BDF). More recently, however, new classes of formulae which can offer some important advantages over BDF have emerged. In particular, some recent large-scale independent comparisons have indicated that modified extended backward differentiation formulae (MEBDF) are particularly efficient for general stiff initial value problems and for linearly implicit DAEs with index ⩽3. In the present paper we survey some of the more important theory associated with these formulae, discuss some of the practical applications where they are particularly effective, e.g., in the solution of damped highly oscillatory problems, and describe some significant recent extensions to the applicability of MEBDF codes.
ISSN:	0377-0427 1879-1778
DOI:	10.1016/S0377-0427(00)00463-5