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. © 2013 Ashyralyev and Yildirim; licensee Springer.
CITATION STYLE
Ashyralyev, A., & Yildirim, O. (2013). On the numerical solution of hyperbolic IBVP with high-order stable finite difference schemes. Boundary Value Problems, 2013. https://doi.org/10.1186/1687-2770-2013-29
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