ОДНОШАГОВЫЕ ЧИСЛЕННЫЕ МЕТОДЫ ДЛЯ РЕШЕНИЯ СМЕШАННЫХ ФУНКЦИОНАЛЬНО-ДИФФЕРЕНЦИАЛЬНЫХ УРАВНЕНИЙ

Translated title of the contribution: One-step numerical methods for mixed functional differential equations

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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.
Translated title of the contributionOne-step numerical methods for mixed functional differential equations
Original languageRussian
Pages (from-to)187-197
Number of pages11
JournalТруды института математики и механики УрО РАН
Volume21
Issue number2
Publication statusPublished - 2015

GRNTI

  • 27.41.00

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