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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Volume 21, Number 2, Pages 187–197
(Mi timm1181)
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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
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.
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
Linking options:
https://www.mathnet.ru/eng/timm1181 https://www.mathnet.ru/eng/timm/v21/i2/p187
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Abstract page: | 288 | Full-text PDF : | 81 | References: | 53 | First page: | 18 |
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