Analysis of generalized backwards difference formula methods applied to Hessenberg form differential-algebraic equations

J. B. Keiper; C. W. Gear

doi:10.1137/0728044

Analysis of generalized backwards difference formula methods applied to Hessenberg form differential-algebraic equations

J. B. Keiper, C. W. Gear

Chemical & Biological Engineering

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

The numerical solution of Hessenberg form differential-algebraic equations by variable stepsize, generalized backward difference formulae (GBDF) is studied. GBDF methods of sufficiently high order are shown to converge for problems of index 3 and 4. The proof techniques developed are not sufficiently powerful to show convergence for index 5 problems, although it is speculated that convergence also occurs for these problems.

Original language	English (US)
Pages (from-to)	833-858
Number of pages	26
Journal	SIAM Journal on Numerical Analysis
Volume	28
Issue number	3
DOIs	https://doi.org/10.1137/0728044
State	Published - 1991

All Science Journal Classification (ASJC) codes

Numerical Analysis
Computational Mathematics
Applied Mathematics

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abstract = "The numerical solution of Hessenberg form differential-algebraic equations by variable stepsize, generalized backward difference formulae (GBDF) is studied. GBDF methods of sufficiently high order are shown to converge for problems of index 3 and 4. The proof techniques developed are not sufficiently powerful to show convergence for index 5 problems, although it is speculated that convergence also occurs for these problems.",

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AB - The numerical solution of Hessenberg form differential-algebraic equations by variable stepsize, generalized backward difference formulae (GBDF) is studied. GBDF methods of sufficiently high order are shown to converge for problems of index 3 and 4. The proof techniques developed are not sufficiently powerful to show convergence for index 5 problems, although it is speculated that convergence also occurs for these problems.

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Analysis of generalized backwards difference formula methods applied to Hessenberg form differential-algebraic equations

Abstract

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