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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Differential-algebraic systems as differential equations on manifolds
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by Werner C. Rheinboldt PDF
Math. Comp. 43 (1984), 473-482 Request permission

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 lower-dimensional manifolds. This class includes systems for which the application of ODE-solvers is known to lead to difficulties. Finally, some solution approach based on continuation techniques is outlined.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Math. Comp. 43 (1984), 473-482
  • MSC: Primary 58F99; Secondary 34A15, 65L99
  • DOI: https://doi.org/10.1090/S0025-5718-1984-0758195-5
  • MathSciNet review: 758195