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. 
@article{DEMR_2018_10_a4,
     author = {M. G. Magomed-Kasumov and S. R. Magomedov},
     title = {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},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {50--60},
     publisher = {mathdoc},
     volume = {10},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DEMR_2018_10_a4/}
}
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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/