Geodesic
The spectral method for solving the Cauchy problem for systems of ordinary differential equations by means of a system of functions orthogonal in the sense of Sobolev, generated by the Haar system
Daghestan Electronic Mathematical Reports, Tome 10 (2018), pp. 50-60.

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We consider an iterative method that numerically solves Cauchy problem for systems of equations. Suggested method is based on using Sobolev orthogonal system of functions, generated by Haar functions $\{1, \chi_n, 2^k n \leq 2^{k+1}, k \geq 1\}$.
Keywords: Cauchy problem, numerical method, Sobolev inner product, system of differential equations, Haar system. 
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M. G. Magomed-Kasumov; S. R. Magomedov. The spectral method for solving the Cauchy problem for systems of ordinary differential equations by means of a system of functions orthogonal in the sense of Sobolev, generated by the Haar system. Daghestan Electronic Mathematical Reports, Tome 10 (2018), pp. 50-60. http://geodesic.mathdoc.fr/item/DEMR_2018_10_a4/

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