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


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Ashyralyev A., Yıldırım Ö.

BOUNDARY VALUE PROBLEMS, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2013
  • Doi Number: 10.1186/1687-2770-2013-29
  • Journal Name: BOUNDARY VALUE PROBLEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Yıldız Technical University Affiliated: Yes

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.