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Open Access Research

On the numerical solution of hyperbolic IBVP with high-order stable finite difference schemes

Allaberen Ashyralyev1 and Ozgur Yildirim2*

Author affiliations

1 Department of Mathematics, Fatih University, Istanbul, 34500, Turkey

2 Department of Mathematics, Yildiz Technical University, Istanbul, 34210, Turkey

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Citation and License

Boundary Value Problems 2013, 2013:29  doi:10.1186/1687-2770-2013-29

Published: 15 February 2013

Abstract

The abstract Cauchy problem for the hyperbolic equation in a Hilbert space H with self-adjoint positive definite operator A is considered. The third and fourth orders of accuracy difference schemes for the approximate solution of this problem are presented. The stability estimates for the solutions of these difference schemes are established. A finite difference method and some results of numerical experiments are presented in order to support theoretical statements.

MSC: 65J10, 65M12, 65N12, 35L30.

Keywords:
abstract hyperbolic equation; stability; initial boundary value problem