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A numerical approach for nonsmooth ordinary differential equations. (English) Zbl 1360.65203

Summary: In this paper, the authors proposed an approach for solving nonsmooth continuous and discontinuous ordinary differential equations which is based on a generalization of the Taylor expansion. First is considered a generalized derivative for nonsmooth functions with a single variable which is proposed by A. V. Kamyad et al. [“A new definition for generalized first derivative of nonsmooth functions”, Appl. Math., Irvine 2, No. 10, 1252–1257 (2011; doi:10.4236/am.2011.210174)]. Then, the generalized Taylor expansion of nonsmooth functions is introduced and used to state an approach. Finally, some numerical examples of nonsmooth ordinary differential equations are solved.

MSC:

65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
46G05 Derivatives of functions in infinite-dimensional spaces
90C56 Derivative-free methods and methods using generalized derivatives
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