Differentialalgebraic systems as differential equations on manifolds
Author:
Werner C. Rheinboldt
Journal:
Math. Comp. 43 (1984), 473482
MSC:
Primary 58F99; Secondary 34A15, 65L99
MathSciNet review:
758195
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Abstract: Based on the theory of differential equations on manifolds, existence and uniqueness results are proved for a class of mixed systems of differential and algebraic equations as they occur in various applications. Both the autonomous and nonautonomous case are considered. Moreover, a class of algebraically incomplete systems is introduced for which existence and uniqueness results only hold on certain lowerdimensional manifolds. This class includes systems for which the application of ODEsolvers is known to lead to difficulties. Finally, some solution approach based on continuation techniques is outlined.
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G. Söderlind, DASP3A Program for the Numerical Integration of Partitioned Stiff ODE's and Differential Algebraic Systems, Tech. Report TRITANA8008, Dept. of Numer. Anal. and Comp. Science, The Royal Inst. of Technology, Stockholm, Sweden, 1980.
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 V. I. Arnold, Ordinary Differential Equations, transl. from the Russian by R. A. Silverman, The MIT Press, Cambridge, Mass., 1981. MR 0361233 (50:13679)
 [2]
 M. Bier, O. A. Palusinski, R. A. Mosher & D. A. Saville, "Electrophoresis: Mathematical modeling and computer simulation," Science, v. 219, 1983, pp. 12811286.
 [3]
 J. P. Fink & W. C. Rheinboldt, "On the discretization error of parametrized nonlinear equations," SIAM J. Numer. Anal., v. 20, 1983, pp. 732746. MR 708454 (85i:65072)
 [4]
 C. W. Gear, "Simultaneous numerical solution of differentialalgebraic equations," IEEE Trans. Circuit Theory, v. CT18, 1971, pp. 8995.
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 C. W. Gear & L. R. Petzold, ODE Methods for the Solution of Differential/Algebraic Systems, Tech. Report 821103, Dept. of Comp. Sci., Univ. of Illinois at UrbanaChampaign, 1982.
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 S. Lang, Introduction to Differentiable Manifolds, Wiley, New York, 1962. MR 0155257 (27:5192)
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 L. Petzold, "Differential/algebraic equations are not ODE's," SIAM J. Sci. Statist. Comput., v. 3, 1982, pp. 367384. MR 667834 (83i:65066)
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 L. R. Petzold, "A description of DASSL: A differential/algebraic system solver," in Proc. IMACS World Congress, Montreal, Canada, Vol. 2, R. Peskin, ed., 1982. MR 751605
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 W. C. Rheinboldt, "Solution fields of nonlinear equations and continuation methods," SIAM J. Numer. Anal., v. 17, 1980, pp. 221237. MR 567270 (81h:65053)
 [10]
 W. C. Rheinboldt & J. V. Burkardt, "A locallyparametrized continuation process," ACM Trans. Math. Software, v. 9, 1983, pp. 215235. MR 715303 (85f:65052)
 [11]
 G. Söderlind, DASP3A Program for the Numerical Integration of Partitioned Stiff ODE's and Differential Algebraic Systems, Tech. Report TRITANA8008, Dept. of Numer. Anal. and Comp. Science, The Royal Inst. of Technology, Stockholm, Sweden, 1980.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198407581955
PII:
S 00255718(1984)07581955
Article copyright:
© Copyright 1984
American Mathematical Society
