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A nonlinear system of differential equations with distributed delays. (English) Zbl 1340.65133

Vejchodský, T. (ed.) et al., Programs and algorithms of numerical mathematics 15. Proceedings of the 15th seminar (PANM), Dolní Maxov, Czech Republic, June 6–11, 2010. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-57-8). 58-64 (2010).
Delay differential equations are differential equations, where the derivative of the solution at time \(t\) depends not only on the solution at time \(t\) but also on the solution at previous times. Such a problem has many applications and the paper describes some of them. The author suggest a numerical method based on a combination of quadrature formula to resolve the delayed information and a standard numerical scheme for ordinary differential equations. The method is tested by a numerical experiment.
For the entire collection see [Zbl 1277.65003].

MSC:

65L03 Numerical methods for functional-differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
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