A New Unconditionally Stable Second Order of Accuracy Difference Scheme for the Time Delay Telegraph Equation

Ashyralyev A., AĞIRSEVEN D., TÜRK K.

Mathematical Methods in the Applied Sciences, cilt.48, sa.18, ss.16540-16551, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 18
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1002/mma.70106
  • Dergi Adı: Mathematical Methods in the Applied Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.16540-16551
  • Anahtar Kelimeler: delay telegraph equation, difference scheme, stability
  • Trakya Üniversitesi Adresli: Evet

Özet

In this paper, we study a new unconditionally stable second order of accuracy difference scheme for the approximate solution of the initial value problem for the time delay telegraph equation in a Hilbert space with self-adjoint positive definite operator. We prove the main theorem on stability of this difference scheme. As an application, we present absolutely stable difference schemes for the approximate solution of two initial-boundary value problems for one-dimensional delay telegraph equation with nonlocal conditions and multidimensional delay telegraph equation with Dirichlet condition. Finally, to support the theoretical result, a numerical example of the initial-boundary value problem for the two-dimensional delay telegraph equation with Dirichlet condition is presented.