Abstract
Necessary and sufficient conditions are given for the solvability of fully implicit index-one and semiexplicit index-two linear time-varying semistate systems of the formA(t)x′+B(t)x=f(t). Using these solvability criteria, we establish the convergence and stability of backward difference formulas (BDF) for solvable semiexplicit index-two systems. In the algebraic variables, these methods exhibit a boundary layer of instability of length 2k, wherek is the order of the method. Finally, we show that the systems considered in this paper belong to a class of problems, solvable by BDF, which strictly contains the systems safely transformable to standard canonical form.
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This research was supported in part by the Air Force Office of Scientific Research under Grant No. AFOSR-84-0240. It constitutes a portion of the author's Ph.D. thesis in Applied Mathematics at North Carolina State University under the direction of Professor Stephen L. Campbell.
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Clark, K.D. The numerical solution of some higher-index time-varying semistate systems by difference methods. Circuits Systems and Signal Process 6, 61–75 (1987). https://doi.org/10.1007/BF01599006
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DOI: https://doi.org/10.1007/BF01599006