Geodesic
A numerical method for solving ordinary differential equations by converting them into the form of a Shannon
Matematičeskoe modelirovanie, Tome 32 (2020) no. 8, pp. 3-20.

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A numerical solution method based on the reduction of systems of ordinary differential equations to the Shannon form is considered. Shannon's equations differ in that they contain only multiplication and summation operations. The absence of functional transformations makes it possible to simplify and unify the process of numerical integration of differential equations in the form of Shannon. To do this, it is enough in the initial equations given in the normal form of Cauchy to make a simple replacement of variables. In contrast to the classical fourth-order Runge-Kutta method, the numerical method under consideration may have a higher order of accuracy.
Keywords: numerical methods, order of accuracy, ordinary differential equations
Mots-clés : Shannon equations. 
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N. G. Chikurov. A numerical method for solving ordinary differential equations by converting them into the form of a Shannon. Matematičeskoe modelirovanie, Tome 32 (2020) no. 8, pp. 3-20. http://geodesic.mathdoc.fr/item/MM_2020_32_8_a0/

[1] C. Shannon, “Mathematical theory of the differential analyzer”, J. Math. and Phys., 20:4 (1941), 337 | DOI | MR | Zbl

[2] K. Shennon, Raboty po teorii informacii i kibernetike, Per. s angl., eds. R.L. Dobrushin, O. B. Lupanov, Izd. inostr. lit., M., 1963, 709 pp.

[3] A. V. Kalyaev, Teoriya tsifrovykh integriruyuschix mashin i struktur, Sovetskoe radio, M., 1970, 471 pp.

[4] E. Khairer, S. Nersett, G. Vanner, Reshenie obyknovennykh differentsialnykh uravnenii. Nezhestkie zadachi, Per. s angl., Mir, M., 1990, 512 pp.; Hairer E., Norset S., Wanner G., Solving ordinary differential equations. Nonstiff problems, Springer-Verlag, Berlin–Heidelberg–New York–London–Paris–Tokyo, 1987 | MR | Zbl

[5] A. M. Gofen, “Bystroe razlozhenie v ryad Tejlora i reshenie zadachi Koshi”, Vychisl. matem. i matem. fiz., 22:5 (1982), 1094–1108 | MR | Zbl

[6] A. A. Samarskij, A. V. Gulin, Chislennye metody, Uch. posobie, Nauka, M., 1989, 432 pp.

[7] E. K. Zholkovskij, A. A. Belov, N. N. Kalitkin, “Reshenie zhestkix zadach Koshi yavnymi skhemami s geometricheski-adaptivnym vyborom shaga”, Preprint IPM im. M.V. Keldysha, 2018, 227, 20 pp.

[8] IU. V. Rakitskij, S. M. Ustinov, I. G. Chernoruczkij, Chislennye metody resheniya zhestkix sistem, Nauka, M., 1979, 208 pp.

[9] Chikurov N.G., “Stability and accuracy of implicit methods for stiff systems of linear differential equations”, Differential Equations, 42 (2006), 1057–1067 | DOI | MR | Zbl

[10] Kalitkin N. N., Chislennye metody, Nauka, M., 1978, 512 pp.