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Stability of ZakianI MN recursions for linear delay differential equations

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Abstract

Long sequences of linear delay differential equations (DDEs) frequently occur in the design of control systems with delays using iterative-numerical methods, such as the method of inequalities. ZakianI MN recursions for DDEs are suitable for solving this class of problems, since they are reliable and provide results to the desired accuracy, economically even if the systems are stiff. This paper investigates the numerical stability property of theI MN recursions with respect to Barwell's concept ofP-stability. The result shows that the recursions using full gradeI MN approximants areP-stable if, and only if,N−2≤M≤N−1.

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  1. Department of Electrical Engineering, Faculty of Engineering, Chulalongkorn University, 10330, Bangkok, Thailand

    Suchin Arunsawatwong

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  1. Suchin Arunsawatwong
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Communicated by Gustaf Söderlind.

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Arunsawatwong, S. Stability of ZakianI MN recursions for linear delay differential equations. Bit Numer Math 38, 219–233 (1998). https://doi.org/10.1007/BF02512363

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  • DOI: https://doi.org/10.1007/BF02512363

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