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DIFFERENTIAL EQUATIONS WITH DELAY: PROPERTIES, METHODS, SOLUTIONS AND MODELS

https://doi.org/10.26583/vestnik.2023.287

Abstract

Ordinary differential equations and partial differential equations with constant and variable delay are considered. Exact, approximate analytical and numerical methods for solving such equations are presented. The most common mathematical models with delay used in population theory, biology, medicine and other applications are described.

About the Author

A. V. Aksenov
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University
Russian Federation


References

1. Polyanin A.D., Sorokin V.G., Zhurov A.I. Differencialnye uravneniya s zapazdyvaniem svojstva meto¬dy-resheniya i modeli [Differential equations with delay: Properties, methods, solutions and models]. Moscow. Institute of Mechanics and Mechanics RAS Publ., 2022 [in Russian].

2. Polyanin A.D., Zhurov A.I. Functional constraints method for constructing exact solutions to delay reaction-diffusion equations and more complex nonlinear equations. Communications in Nonlinear Science and Numerical Simulation, 2014. Vol. 19. No. 3. Pp. 417–430.

3. Polyanin A.D., Zhurov A.I. New generalized and functional separable solutions to non-linear delay reaction-diffusion equations. International Journal of Non-Linear Mechanics, 2014. Vol. 59. Pp. 16–22.

4. Polyanin A.D., Sorokin V.G. Nonlinear pantograph-type diffusion PDEs: Exact solutions and the principle of analogy. Mathematics, 2021. Vol. 9. No. 5. P. 511.

5. Aksenov A.V., Polyanin A.D. Methods for constructing complex solutions of nonlinear PDEs using simpler solutions. Mathematics, 2021. Vol. 9. No. 4. P. 345.

6. Aksenov A.V., Polyanin A.D. Review of methods for constructing exact solutions of equations of mathematical physics based on simpler solutions. Theoretical and Mathematical Physics, 2022. Vol. 211. No. 2. Pp. 567–594.


Review

For citations:


Aksenov A.V. DIFFERENTIAL EQUATIONS WITH DELAY: PROPERTIES, METHODS, SOLUTIONS AND MODELS. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2023;12(3):187-190. (In Russ.) https://doi.org/10.26583/vestnik.2023.287

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ISSN 2304-487X (Print)