Analysis of inverse problem for pseudo-hyperbolic equation under periodic boundary condition

BAĞLAN İ., Yernazar A., ASLAN E., BUDAK H., Vivas-Cortez M.

Scientific Reports, cilt.15, sa.1, 2025 (SCI-Expanded, Scopus) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1038/s41598-025-25105-1
  • Dergi Adı: Scientific Reports
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, BIOSIS, Chemical Abstracts Core, MEDLINE, Directory of Open Access Journals
  • Anahtar Kelimeler: Finite difference method, Fourier method, Inverse problem, Nonlinear pseudo-hyperbolic equation, Periodic boundary condition
  • Kocaeli Üniversitesi Adresli: Evet

Özet

This research paper investigates an inverse problem involving time-dependent unknown coefficients in a one-dimensional nonlinear pseudo-hyperbolic equation with nonlocal boundary conditions. The Fourier method is employed, and the convergence, uniqueness, and stability of the solution are demonstrated. Additionally, the Finite Difference Method (FDM) is applied to address the inverse problem numerically. A numerical example is provided to demonstrate the performance of the method. In the Finite Difference Method, two finite difference schemes with different levels of accuracy are used and compared with each other. Furthermore, the cases of ε = 0 (hyperbolic) and ε ≠ 0 (pseudo-hyperbolic) are also compared.