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The Analysis of Generalized Backwards Difference Formula Methods Applied to Hessenberg Form Differential-Algebraic Equations

J. B. Keiper and C. W. Gear
SIAM Journal on Numerical Analysis
Vol. 28, No. 3 (Jun., 1991), pp. 833-858
Stable URL: http://www.jstor.org/stable/2157731
Page Count: 26
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The Analysis of Generalized Backwards Difference Formula Methods Applied to Hessenberg Form Differential-Algebraic Equations
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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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