Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Lukomskii D. S., Lukomskii S. F., Terekhin P. A. Solution of Cauchy Problem for Equation First Order Via Haar Functions. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 2, pp. 151-159. DOI: 10.18500/1816-9791-2016-16-2-151-159, EDN: WCNQID

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
Full text:
(downloads: 182)

Solution of Cauchy Problem for Equation First Order Via Haar Functions

Lukomskii Dmitry Sergeyevich, Saratov State University
Lukomskii Sergei Feodorovich, Saratov State University
Terekhin Pavel A., Saratov State University

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.

  1. Ohkita M., Kobayashi Y. An application of rationalized Haar functions to solution of linear differential equations // IEEE Transactions on Circuit and Systems. 1968. Vol. 33, iss. 9. P. 853–862.
  2. Razzaghi M., Ordokhani Y. Solution of differential equations via rationalized Haar functions // Mathematics and computers in simulation. 2001. Vol. 56, iss. 3. P. 235–246.
  3. Razzaghi M., Ordokhani Y. An application of rationalized Haar functions for variational problems // Applied Mathematics and Computation. 2001. Vol. 122, iss. 3. P. 353–364.
  4. Lukomskii D. S. Primenenie sistemy Haara dlya resheniya zadachi Koshi [Application of Haar system for solving the Cauchy problem]. Matematika. Mehanika [Mathematics. Mechanics], Saratov, Saratov Univ. Press, 2014, iss. 14, pp. 47–50 (in Russian).
  5. Lukomskii D. S., Terekhin P. A. Ob ocenke pogreshnosti resheniya zadachi Koshi s pomosch’yu sistem sjatiy i sdvigov [An error estimate for the Cauchy problem by using compression systems and shifts]. Trudy Matematicheskogo centra imeni N. I. Lobachevskogo [Proceedings of the Mathematical Centre named N. I. Lobachevsky]. Kazan, Kazan Matnematical Society, 2015, vol. 51, pp. 295–297 (in Russian).