High-accuracy collocation approach with 8th-order B-splines for the 7th-order KdV equation
Computational and Applied Mathematics, cilt.46, sa.3, 2027 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 46 Sayı: 3
- Basım Tarihi: 2027
- Doi Numarası: 10.1007/s40314-026-03939-3
- Dergi Adı: Computational and Applied Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, Compendex, zbMATH, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: 8th order B-splines, Collocation, Kaup kuperschmidt equation, Lax equation, Sawada–Kotera equation
- İstanbul Medipol Üniversitesi Adresli: Evet
Özet
In this work, an 8th-degree B-spline collocation numerical scheme is presented for the solution of the 7th-order nonlinear Korteweg–de Vries (KdV) equation. Based on the utilization of highly smooth and continuous octic spline functions, the scheme has improved spatial resolution, which is effective in resolving the complicated dispersive dynamics that are inherent in high-order wave models. The nonlinear term is treated using a Taylor series linearization whereas temporal marching is addressed using a backward Crank–Nicolson approach. To evaluate the performance of the technique, it is used for benchmark 7th-order integrable KdV equations, i.e., those of Lax, Kaup–Kuperschmidt, and Sawada–Kotera. The obtained results exhibit very good agreement with exact references and yield reduced maximum norm errors in comparison with already published results. The numerical results demonstrate the accuracy of the proposed octic spline-based approach.