2017
Том 69
№ 9

All Issues

On a class of computation algorithms for approximate integration of ordinary differential equations with initial conditions

Bondarenko P. S.

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Abstract

The author first introduces the concepts of computation and real computation algorithms for approximate integration, by the method of finite differences, of systems of ordinary differential equations with initial conditions and investigates the general properties of these algorithms, in particular the property of their stability.
Then a study is made of the class of computation algorithms based on methods of the Euler, Runge and Adams type for numerical integration of these equations, and it is shown that this class of computation algorithms makes it possible to determine with sufficient precision the guaranteed interval of existence of the solution sought for, to estimate the position of the graph of this solution and to find a guaranteed real estimate of the error of the numerical solution obtained.

Citation Example: Bondarenko P. S. On a class of computation algorithms for approximate integration of ordinary differential equations with initial conditions // Ukr. Mat. Zh. - 1961. - 13, № 1. - pp. 3-21.

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