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Numerical methods for integral dynamic models with nonlinear delays

TitleNumerical methods for integral dynamic models with nonlinear delays
AuthorsA. N. Tynda1, D. N. Sidorov2, I. R. Muftahov3
1Penza State University
2Melentiev Energy System Institute SB RAS
3Main Computing Center of Joint Stock Company «Russian Railways»
AnnotationThe 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.
KeywordsVolterra integral equations, discontinuous kernels, nonlinear delays, regularization, Newton-Kantorovich method, adaptive meshes
CitationTynda 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: 15.10.2019.