Numerical approaches for solution of hyperbolic difference equations on circle

Ashyralyev A., Hezenci F., SÖZEN Y.

Georgian Mathematical Journal, vol.31, no.5, pp.723-730, 2024 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 31 Issue: 5
  • Publication Date: 2024
  • Doi Number: 10.1515/gmj-2023-2103
  • Journal Name: Georgian Mathematical Journal
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.723-730
  • Keywords: Difference equations on manifolds, difference schemes, self-adjoint positive definite operator, well-posedness
  • Hacettepe University Affiliated: Yes

Abstract

The present paper considers nonlocal boundary value problems for hyperbolic equations on the circle T 1 \mathbb{T}^{1}. The first-order modified difference scheme for the numerical solution of nonlocal boundary value problems for hyperbolic equations on a circle is presented. The stability and coercivity estimates in various Hölder norms for solutions of the difference schemes are established. Moreover, numerical examples are provided.