
This article is cited in 1 scientific paper (total in 1 paper)
Software package for the numerical solution of systems of essentially nonlinear ordinary integrodifferentialalgebraic equations
N. G. Bandurin^{}, N. A. Gureeva^{} ^{} Volgograd State University of Architecture and Civil Engineering
Abstract:
Method, algorithm and software package for automatic solution of ordinary nonlinear
integrodifferentialalgebraic equations (IDAE) of sufficiently general form is briefly described. Under
the automatic solution the author understands getting result without executing the stages of selecting
method, of programming and program checking. There are solved both initial and boundary tasks for such equations. It is assumed that the complete set of boundary and initial conditions at the beginning of interval of integration was set. In consequence of differentiation the system of IDAE can be modified into system of ordinary in common essentially nonlinear differential equations (IDE). The problem of finding solving of the system mentioned above on the constant mesh of the interval of integration is posed in two forms — as solving of the system of IDAE and as solving of the appropriate system of IDE, where the developed program should be used. With the purpose of reducing of the system of IDAE and system of IDE to the systems of ordinary
nonlinear algebraic equations at every stage of solving in the algorithm integration formulas and differentiation formulas invented by the author are correspondingly used. Systems like those test systems of both nonlinear IDAE and IDE, which were cited in this investigation, are solved by using of programmes. It is evident that coincidence of results of solving of one and the same system of equations in its different forms can serve as a good evidence of correctness of the results which are got.
Keywords:
integraldifferentialalgebraic equations, numerical methods, nonlinear tasks, computer programs.
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English version:
Mathematical Models and Computer Simulations, 2012, 4:5, 455–463
Bibliographic databases:
UDC:
519.62 Received: 14.12.2010
Citation:
N. G. Bandurin, N. A. Gureeva, “Software package for the numerical solution of systems of essentially nonlinear ordinary integrodifferentialalgebraic equations”, Matem. Mod., 24:2 (2012), 3–16; Math. Models Comput. Simul., 4:5 (2012), 455–463
Citation in format AMSBIB
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\by N.~G.~Bandurin, N.~A.~Gureeva
\paper Software package for the numerical solution of systems of essentially nonlinear ordinary integrodifferentialalgebraic equations
\jour Matem. Mod.
\yr 2012
\vol 24
\issue 2
\pages 316
\mathnet{http://mi.mathnet.ru/mm3203}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=2977118}
\elib{http://elibrary.ru/item.asp?id=21276722}
\transl
\jour Math. Models Comput. Simul.
\yr 2012
\vol 4
\issue 5
\pages 455463
\crossref{https://doi.org/10.1134/S2070048212050031}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2s2.084928982916}
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http://mi.mathnet.ru/eng/mm3203 http://mi.mathnet.ru/eng/mm/v24/i2/p3
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This publication is cited in the following articles:

Bandurin N.G., “Programma dlya avtomaticheskogo resheniya sistem suschestvenno nelineinykh differentsialnoalgebraicheskikh uravnenii (dvumernye zadachi)”, Izv. Volgogradskogo gos. tekhnich. unta, 10:14 (2012), 10–13

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