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On the convergence of the method of finite differences applied to the solution of the initial value problem for functional-differential neutral type equations

Published online by Cambridge University Press:  14 November 2011

N. G. Kazakova  and
D. D. Bainov
N. G. Kazakova
Affiliation:
University of Plovdiv, Plovdiv, Bulgaria
D. D. Bainov
Affiliation:
University of Plovdiv, Plovdiv, Bulgaria
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Synopsis

When solving practically the neutral type equations the derivatives are replaced by finite differences while the members of integral type are replaced by quadrature formulae. The paper deals with the convergence of a natural class of methods applied to the Cauchy problem for functional-differential neutral type equations. It is not obligatory for the approximated operators to be compact.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 89 , Issue 3-4 , 1981 , pp. 259 - 265
Copyright
Copyright © Royal Society of Edinburgh 1981

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References

1Vainikko, G. M.. Analysis of discreting methods. (Russian) (Tartu, 1976).Google Scholar
2Vainikko, G. M.. On the convergence of the difference method for finding out periodic solutions of the ordinary differential equations. (Russian) ž. Vyčisl. Mat. i Mat. Fiz. 15 (1975), 87–100.Google Scholar
3Saarniit, I. R.. An estimation of the convergence of the finite-difference method in case of differential equations with transformed argument. (Russian) Učen. Zap. Tartur. Gos. Univ. 277 (1971), 205–216.Google Scholar
4Saarniit, I. R.. Construction and h-schemes for the linear boundary value problem for differential equations of second order with transformed argument. (Russian) ž. Vyčisl. Mat. i Mat. Fiz. 12 (1972), 105–111.Google Scholar
5Saarniit, I. R.. On solving the boundary value problem for differential equations with transformed argument by means of the finite-difference method. (Russian) ž. Vyčisl. Mat. i Mat. Fiz. 16 (1976), 372–384.Google Scholar
6Sadovskii, B. N.. Ultimately compact and condensating operators. (Russian) Uspehi Mat. Nauk. 27 vyp. 1 (163), (1972), 81–146.Google Scholar
7Vainikko, G. M. and Karma, O. O.. On the convergence of approximation methods for solving linear and non-linear operator equations. (Russian) ž. Vyčisl. Mat. iMat. Fiz. 14 (1974), 828–837.Google Scholar