On the unique weak solvability of second-order unconditionally stable difference scheme for the system of sine-Gordon equations

Creative Commons License

YILDIRIM Ö.

Nonlinear Analysis: Modelling and Control, cilt.29, sa.2, ss.244-264, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 29 Sayı: 2
  • Basım Tarihi: 2024
  • Doi Numarası: 10.15388/namc.2024.29.34196
  • Dergi Adı: Nonlinear Analysis: Modelling and Control
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH, Directory of Open Access Journals
  • Sayfa Sayıları: ss.244-264
  • Anahtar Kelimeler: difference schemes, fixed point theory, stability, weak solvability
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In the present paper, a nonlinear system of sine-Gordon equations that describes the DNA dynamics is considered. A novel unconditionally stable second-order accuracy difference scheme corresponding to the system of sine-Gordon equations is presented. In this work, for the first time in the literature, weak solution of this difference scheme is studied. The existence and uniqueness of the weak solution for the difference scheme are proved in the space of distributions, and the methods of variational calculus are applied. The finite-difference method and the fixed point theory are used in combination to perform numerical experiments that verify the theoretical statements.