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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Volume 21, Number 2, Pages 187–197 (Mi timm1181)  

One-step numerical methods for mixed functional differential equations

V. G. Pimenovab, M. A. Panacheva

a Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
References:
Abstract: First-order partial differential equations are reduced to ordinary differential equations by the method of characteristics. If there is a delay in the original equation, a similar method reduces the equation to a mixed functional differential equation with influence effects in the space variable and with time heredity. We present schemes of one-step multistage methods (analogs of explicit Runge-Kutta methods) for the numerical solution of mixed functional differential equations with the use of two-dimensional interpolation by degenerate splines. Orders of convergence are studied and results of numerical experiments on test examples are given.
Keywords: mixed functional differential equations, numerical algorithm, two-dimensional interpolation, extrapolation, convergence.
Bibliographic databases:
Document Type: Article
UDC: 519.62
Language: Russian
Citation: V. G. Pimenov, M. A. Panachev, “One-step numerical methods for mixed functional differential equations”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 2, 2015, 187–197
Citation in format AMSBIB
\Bibitem{PimPan15}
\by V.~G.~Pimenov, M.~A.~Panachev
\paper One-step numerical methods for mixed functional differential equations
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2015
\vol 21
\issue 2
\pages 187--197
\mathnet{http://mi.mathnet.ru/timm1181}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3408889}
\elib{https://elibrary.ru/item.asp?id=23607931}
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  • https://www.mathnet.ru/eng/timm/v21/i2/p187
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