Numerical solution and error analysis of the fractional nonlinear hyperbolic wave equation using the finite difference method
AIMS Mathematics, cilt.11, sa.10, ss.34963-34974, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 11 Sayı: 10
- Basım Tarihi: 2026
- Doi Numarası: 10.3934/math.20261361
- Dergi Adı: AIMS Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.34963-34974
- Anahtar Kelimeler: error estimation, finite difference method, fractional nonlinear wave equation, L2-1σ memory coefficients, numerical analysis
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Hakkari Üniversitesi Adresli: Evet
Özet
In this work, we examined the numerical results for a nonlinear fractional hyperbolic-type wave equation governed by a time-fractional derivative of order α. For the fractional term, an L2-1σ memory discretization approach was integrated with standard central difference approximations of spatial second-order derivatives. Explicitly, the study formulates the discrete algebraic relations for the governing system, proves the comprehensive numerical scheme, and evaluates computational efficiency and accuracy across diverse spatial grid refinements.