Solving a Sequence of Recurrence Relations for First-Order Differential Equations

Andrey Batukhtin; Irina Batukhtina; Maxim Bass; Sergey Batukhtin; Pavel Safronov; Marina Baranovskaya

doi:10.12973/ejmste/79043

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Andrey Batukhtin ¹ ^* , Irina Batukhtina ¹, Maxim Bass ¹, Sergey Batukhtin ¹, Pavel Safronov ¹, Marina Baranovskaya ¹

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¹ Transbaikal State University, RUSSIA^* Corresponding Author

Abstract

A whole category of engineering and economic problems can be reduced to solving a set of differential equations. Downsides of known approaches for their solutions include limited accuracy numerical methods with stringent requirements for computational power. A direct analytical solution should be derived to eliminate such flaws. This research intends to derive such a solution for an n-dimensional set of recurrence relations for first-order differential equations, linearly dependent on the right side. The research methodology relies on successive integration of the considered set in view of the initial conditions. The overall solution was derived as a sum of products of exponential multipliers with constant coefficients that are defined through weights of a tree graph, which is a descriptor of successive integration. An analytical solution for an n-dimensional set of recurrent differential equations in view of the initial conditions has been derived for the first time in this research.

Keywords

analytical condition
differential equations
differentiation
initial conditions

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 13, Issue 11, November 2017, 7179-7191

https://doi.org/10.12973/ejmste/79043

Publication date: 24 Oct 2017

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How to cite this article

APA

Batukhtin, A., Batukhtina, I., Bass, M., Batukhtin, S., Safronov, P., & Baranovskaya, M. (2017). Solving a Sequence of Recurrence Relations for First-Order Differential Equations. Eurasia Journal of Mathematics, Science and Technology Education, 13(11), 7179-7191. https://doi.org/10.12973/ejmste/79043

Vancouver

Batukhtin A, Batukhtina I, Bass M, Batukhtin S, Safronov P, Baranovskaya M. Solving a Sequence of Recurrence Relations for First-Order Differential Equations. EURASIA J Math Sci Tech Ed. 2017;13(11):7179-91. https://doi.org/10.12973/ejmste/79043

AMA

Batukhtin A, Batukhtina I, Bass M, Batukhtin S, Safronov P, Baranovskaya M. Solving a Sequence of Recurrence Relations for First-Order Differential Equations. EURASIA J Math Sci Tech Ed. 2017;13(11), 7179-7191. https://doi.org/10.12973/ejmste/79043

Chicago

Batukhtin, Andrey, Irina Batukhtina, Maxim Bass, Sergey Batukhtin, Pavel Safronov, and Marina Baranovskaya. "Solving a Sequence of Recurrence Relations for First-Order Differential Equations". Eurasia Journal of Mathematics, Science and Technology Education 2017 13 no. 11 (2017): 7179-7191. https://doi.org/10.12973/ejmste/79043

Harvard

Batukhtin, A., Batukhtina, I., Bass, M., Batukhtin, S., Safronov, P., and Baranovskaya, M. (2017). Solving a Sequence of Recurrence Relations for First-Order Differential Equations. Eurasia Journal of Mathematics, Science and Technology Education, 13(11), pp. 7179-7191. https://doi.org/10.12973/ejmste/79043

MLA

Batukhtin, Andrey et al. "Solving a Sequence of Recurrence Relations for First-Order Differential Equations". Eurasia Journal of Mathematics, Science and Technology Education, vol. 13, no. 11, 2017, pp. 7179-7191. https://doi.org/10.12973/ejmste/79043