IJPAM: Volume 109, No. 4 (2016)

NUMERICAL SOLUTION TO INITIAL VALUE PROBLEM
FOR ONE CLASS OF DIFFERENTIAL EQUATION
WITH MAXIMUM

Sergey N. Dashkovskiy$^1$, Olga D. Kichmarenko$^2$,
Kateryna Yu. Sapozhnikova$^3$, Alexander N. Vityuk$^4$
$^1$University of Würzburg
Sanderring 2, 97070 Würzburg, GERMANY
$^{2,4}$Odesa National I.I. Mechnikov University
2, Dvorianska, Odessa, 65000, UKRAINE
$^3$University of Applied Sciences Erfurt
Altonaer Str. 25, 99085 Erfurt, GERMANY

Abstract. This paper presents a numerical method for solution computation for one type of initial value problems given by differential equations with maximum of the unknown function over a prehistory. We prove the convergence of the method and illustrate it by several examples.

Received: May 11, 2016

Revised: October 1, 2016

Published: October 9, 2016

AMS Subject Classification: 34K, 37M99

Key Words and Phrases: differential equations with maximum, numerical methods, nonlinear systems
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DOI: 10.12732/ijpam.v109i4.20 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 4
Pages: 1015 - 1027


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