Nonlinear Systems of Volterra Equations with Piecewise Smooth Kernels: Numerical Solution and Application for Power Systems Operation
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 pap...
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MDPI AG
2020-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/8/1257 |
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| author | Denis Sidorov Aleksandr Tynda Ildar Muftahov Aliona Dreglea Fang Liu |
| author_facet | Denis Sidorov Aleksandr Tynda Ildar Muftahov Aliona Dreglea Fang Liu |
| author_sort | Denis Sidorov |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T18:03:02Z |
| format | Article |
| id | doaj.art-4ac07cd2a68b43f4b87e8f4da0e2cbe7 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T18:03:02Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-4ac07cd2a68b43f4b87e8f4da0e2cbe72023-11-20T08:44:36ZengMDPI AGMathematics2227-73902020-08-0188125710.3390/math8081257Nonlinear Systems of Volterra Equations with Piecewise Smooth Kernels: Numerical Solution and Application for Power Systems OperationDenis Sidorov0Aleksandr Tynda1Ildar Muftahov2Aliona Dreglea3Fang Liu4Applied Mathematics Department, Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664033 Irkutsk, RussiaFaculty of Computer Engineering, Penza State University, 440026 Penza, RussiaApplied Mathematics Department, Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664033 Irkutsk, RussiaApplied Mathematics Department, Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664033 Irkutsk, RussiaSchool of Automation, Central South University, Changsha 410083, ChinaThe 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.https://www.mdpi.com/2227-7390/8/8/1257inverse problemNewton–Kantorovich methodnonlinear Volterra equationsdiscontinuous kernelsenergy storagedirect discretization |
| spellingShingle | Denis Sidorov Aleksandr Tynda Ildar Muftahov Aliona Dreglea Fang Liu Nonlinear Systems of Volterra Equations with Piecewise Smooth Kernels: Numerical Solution and Application for Power Systems Operation Mathematics inverse problem Newton–Kantorovich method nonlinear Volterra equations discontinuous kernels energy storage direct discretization |
| title | Nonlinear Systems of Volterra Equations with Piecewise Smooth Kernels: Numerical Solution and Application for Power Systems Operation |
| title_full | Nonlinear Systems of Volterra Equations with Piecewise Smooth Kernels: Numerical Solution and Application for Power Systems Operation |
| title_fullStr | Nonlinear Systems of Volterra Equations with Piecewise Smooth Kernels: Numerical Solution and Application for Power Systems Operation |
| title_full_unstemmed | Nonlinear Systems of Volterra Equations with Piecewise Smooth Kernels: Numerical Solution and Application for Power Systems Operation |
| title_short | Nonlinear Systems of Volterra Equations with Piecewise Smooth Kernels: Numerical Solution and Application for Power Systems Operation |
| title_sort | nonlinear systems of volterra equations with piecewise smooth kernels numerical solution and application for power systems operation |
| topic | inverse problem Newton–Kantorovich method nonlinear Volterra equations discontinuous kernels energy storage direct discretization |
| url | https://www.mdpi.com/2227-7390/8/8/1257 |
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