Geodesic
One-step numerical methods for mixed functional differential equations
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 2, pp. 187-197

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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
Mots-clés : extrapolation, convergence. 
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     author = {V. G. Pimenov and M. A. Panachev},
     title = {One-step numerical methods for mixed functional differential equations},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {187--197},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_2_a15/}
}
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V. G. Pimenov; M. A. Panachev. One-step numerical methods for mixed functional differential equations. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 2, pp. 187-197. http://geodesic.mathdoc.fr/item/TIMM_2015_21_2_a15/