Geodesic
Elementary differentals, their graphs and codes
Matematičeskoe modelirovanie, Tome 21 (2009) no. 8, pp. 37-43 Cet article a éte moissonné depuis la source Math-Net.Ru

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Many tens or hundreds of elementary differentials must be taken into account in constructing one-step numerical methods for solving ODE (like Runge–Kutta methods, Rosenbrock methods, ABC-schemes) of high order accuracy. Their graphical representation in use nowadays does not allow to computerize the huge amount of manual labor. We propose a simple and intuitive way for digital encoding of them and algorithms for generation, analysis and synthesis of these codes. These algorithms are implemented in a computer program that computes tables of codes for elementary differentials up to arbitrary order, together with their multiplicities and gamma-factors. 
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A. V. Tygliyan; S. S. Filippov. Elementary differentals, their graphs and codes. Matematičeskoe modelirovanie, Tome 21 (2009) no. 8, pp. 37-43. http://geodesic.mathdoc.fr/item/MM_2009_21_8_a3/

[1] E. Khairer, S. Nersett, G. Vanner, Reshenie obyknovennykh differentsialnykh uravnenii. Nezhestkie zadachi, Mir, M., 1990 | MR

[2] E. Khairer, G. Vanner, Reshenie obyknovennykh differentsialnykh uravnenii. Zhestkie i differentsialno-algebraicheskie zadachi, Mir, M., 1999

[3] S. S. Filippov, “ABC-skhemy dlya zhestkikh sistem obyknovennykh differentsialnykh uravnenii”, Doklady RAN, 399:2 (2004), 170–172 | MR