Cite this article as:

Lukomskii D. S., Lukomskii S. F., Terekhin P. A. Solution of Cauchy Problem for Equation First Order Via Haar Functions. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2016, vol. 16, iss. 2, pp. 151-159. DOI: https://doi.org/10.18500/1816-9791-2016-16-2-151-159

Language: 
Russian
Heading: 
Mathematics
UDC: 
519.62

Solution of Cauchy Problem for Equation First Order Via Haar Functions

Authors: 
Lukomskii Dmitry Sergeyevich , Saratov State University, Russia, Saratov, Astrakhanskaya 83 , lukomskiids@info.sgu.ru
Lukomskii Sergei Feodorovich, Saratov State University 1, Saratov State University, Russia, 410012, Saratov, Astrahanskaya st., 83 , LukomskiiSF@info.sgu.ru
Terekhin Pavel Alexandrovich, Saratov State University, Russia, Saratov, Astrakhanskaya 83 , TerekhinPA@info.sgu.ru
Abstract: 

In this article we consider a Cauchy problem for the first order differential equation and are looking for its numerical solution. For this aim we represent the derivative of the solution as Haar decomposition. We also obtain estimates of approximate solution. The method is computationally simple and applications are demonstrated through illustrative examples. These examples show that in some cases the error of the proposed method is much less, than in second order Runge – Kutta method.

Key words: 
differential equations, numerical methods, approximate solution, approximation error, Haar system
DOI: 
https://doi.org/10.18500/1816-9791-2016-16-2-151-159
References

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