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A new stability analysis for a class of nonlinear delay differential-algebraic equations and implicit Euler methods. (English) Zbl 1424.65102

Summary: The aim of this paper is mainly to solve nonlinear problems through linearization. Although the linearization process is local, under certain conditions, linearization within the local neighborhood of some solution may not affect the original equations. Based on this idea, we consider the stability and asymptotic stability of a class of nonlinear delay differential-algebraic equations and numerical methods of implicit Euler methods by means of linearization process. Sufficient conditions for stability and asymptotic stability are obtained.

MSC:

65L07 Numerical investigation of stability of solutions to ordinary differential equations
65L80 Numerical methods for differential-algebraic equations
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