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

Boundary value problems

Allaberen Ashyralyev¹  Ozgur Yildirim² 

[1] Department of Mathematics, Fatih University, Istanbul, Turkey;Department of Mathematics, Yildiz Technical University, Istanbul, Turkey

关键词: abstract hyperbolic equation;    stability;    initial boundary value problem;   

DOI  :  10.1186/1687-2770-2013-29

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY