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Article

Nonlinear Systems of Volterra Equations with Piecewise Smooth Kernels: Numerical Solution and Application for Power Systems Operation

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Applied Mathematics Department, Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664033 Irkutsk, Russia
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Baikal School of BRICS, Irkutsk National Research Technical University, 664074 Irkutsk, Russia
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Faculty of Computer Engineering, Penza State University, 440026 Penza, Russia
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Main Computing Center, Joint Stock Company “Russian Railways”, 664005 Irkutsk, Russia
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School of Automation, Central South University, Changsha 410083, China
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Authors to whom correspondence should be addressed.
Mathematics 2020, 8(8), 1257; https://doi.org/10.3390/math8081257
Received: 23 July 2020 / Revised: 27 July 2020 / Accepted: 30 July 2020 / Published: 1 August 2020
(This article belongs to the Section Engineering Mathematics)
The evolutionary integral dynamical models of storage systems are addressed. Such models are based on systems of weakly regular nonlinear Volterra integral equations with piecewise smooth kernels. These equations can have non-unique solutions that depend on free parameters. The objective of this paper was two-fold. First, the iterative numerical method based on the modified Newton–Kantorovich iterative process is proposed for a solution of the nonlinear systems of such weakly regular Volterra equations. Second, the proposed numerical method was tested both on synthetic examples and real world problems related to the dynamic analysis of microgrids with energy storage systems. View Full-Text
Keywords: inverse problem; Newton–Kantorovich method; nonlinear Volterra equations; discontinuous kernels; energy storage; direct discretization; load leveling; polynomial-collocation scheme; midpoint rectangles inverse problem; Newton–Kantorovich method; nonlinear Volterra equations; discontinuous kernels; energy storage; direct discretization; load leveling; polynomial-collocation scheme; midpoint rectangles
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MDPI and ACS Style

Sidorov, D.; Tynda, A.; Muftahov, I.; Dreglea, A.; Liu, F. Nonlinear Systems of Volterra Equations with Piecewise Smooth Kernels: Numerical Solution and Application for Power Systems Operation. Mathematics 2020, 8, 1257. https://doi.org/10.3390/math8081257

AMA Style

Sidorov D, Tynda A, Muftahov I, Dreglea A, Liu F. Nonlinear Systems of Volterra Equations with Piecewise Smooth Kernels: Numerical Solution and Application for Power Systems Operation. Mathematics. 2020; 8(8):1257. https://doi.org/10.3390/math8081257

Chicago/Turabian Style

Sidorov, Denis, Aleksandr Tynda, Ildar Muftahov, Aliona Dreglea, and Fang Liu. 2020. "Nonlinear Systems of Volterra Equations with Piecewise Smooth Kernels: Numerical Solution and Application for Power Systems Operation" Mathematics 8, no. 8: 1257. https://doi.org/10.3390/math8081257

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