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On Difference and Shooting Methods for Boundary Value Problems in Differential‐Algebraic Equations
Author(s) -
März R.
Publication year - 1984
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19840641108
Subject(s) - mathematics , shooting method , differential algebraic equation , boundary value problem , mathematical analysis , algebraic equation , differential equation , differential algebraic geometry , nonlinear system , numerical partial differential equations , ordinary differential equation , physics , quantum mechanics
Isolatedly solvable boundary value problems are formulated for implicit nonlinear differential‐algebraic equations which can be partitioned into coupled non‐singular differential equations and finite‐dimensional equations. Then, for solving these problems by shooting methods, the behaviour of the shooting equations is investigated. The null‐space of the Jacobian of the shooting mapping is constant in a neighbourhood of the solution. Newton methods are applicable for shooting. Further, the convergence of some general difference methods for boundary problems in differential‐algebraic equations is proved. Especially, it is shown that the trapezoidal rule and the centered Euler method which are applied to the differential‐algebraic equation directly, become instable.