**MSC2010** 65R20, 37N40

### Numerical methods for the problems of nonlinear macroeconomic integral models

#### A. N. Tynda^{1}, N. Yu. Kudryashova^{2}

Annotation | In this paper we suggest several methods for numerical treatment of integral dynamical systems described by nonlinear integral equations of the special form. The first group of problems is connected with solution of nonlinear integral Volterra-type equations’ system with unknown function placed at the lower limits of integration. Two effective methods for solution of such systems are suggested. The first method is direct. The second method is iterative; it is based on the linearization of the integral operators using modified Newton-Kantorovich scheme. The second group of problems is connected with the optimal control problems in macroeconomical VCM models. We suggest two original approaches to these problems’ solution; these approaches allow to determine the extremals of functionals in the first approximation. Proposed algorithms also allow to obtain more accurate approximations. In the conclusion several numerical results for model problems are stated. These results allow to judge the effectiveness of the proposed approaches. |
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Keywords | Systems of nonlinear integral equations, VCM models, Newton-Kantorovich method, nonlinear delays, extremal of functional, approximation of integrals. |

^{1}**Aleksandr N. Tynda**, Associate Professor, Department of Higher and Applied Mathematics, Penza State University (40 Krasnaya Str., Penza 440026, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0001-6023-9847, tyndaan@mail.ru^{2}**Natalia Yu. Kudryashova**, Associate Professor, Department of Higher and Applied Mathematics, Penza State University (40 Krasnaya Str., Penza 440026, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0002-0789-4559, math.kudryashova@yandex.ru

**Citation**: A. N. Tynda, N. Yu. Kudryashova, "[Numerical methods for the problems of nonlinear macroeconomic integral models]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,19:4 (2017) 79–94 (In Russian)

**DOI** 10.15507/2079-6900.19.201704.79-94