Title | Numerical methods for integral dynamic models with nonlinear delays |
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Authors | A. N. Tynda^{1}, D. N. Sidorov^{2}, I. R. Muftahov^{3}^{1}Penza State University ^{2}Melentiev Energy System Institute SB RAS ^{3}Main
Computing Center of Joint Stock Company «Russian Railways» |

Annotation | The paper is dedicated to numerical investigation of integral dynamic systems used in macroeconomics, renewal theory, automatic control theory and so forth. The linear and nonlinear Volterra integral equations and its systems of the special form are applied in such integral models. In particular, we investigate nonlinear integral equations of the first kind whose kernels have jump discontinuities along the set of smooth curves and the systems of integral equations with unknown functions in the limits of integration. We construct a family of direct and iterative numerical methods for such equations. Also some numerical approaches to optimization problems in systems with nonlinear delays are suggested. In conclusion we consider a nonlinear Volterra integral model arising in hydroenergetics. |

Keywords | Volterra integral equations, discontinuous kernels, nonlinear delays, regularization, Newton-Kantorovich method, adaptive meshes |

Citation | Tynda A. N., Sidorov D. N., Muftahov I. R. ''Numerical methods for integral dynamic models with nonlinear delays'' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 311-317. Available at: http://conf.svmo.ru/files/deamm2017/papers/paper43.pdf. - Date of access: 24.06.2019. |

**© SVMO, National Research Mordovia State University, 2019**

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