A computational method for nonlinear Burgers’ equation using quartic-trigonometric tension B-splines

Yigit G., ERSOY HEPSON Ö., Allahviranloo T.

Mathematical Sciences, cilt.18, sa.1, ss.17-28, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s40096-022-00481-1
  • Dergi Adı: Mathematical Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.17-28
  • Anahtar Kelimeler: Quartic-trigonometric tension B-spline, Galerkin method, Stability analysis, Burgers' equation, Wave motion, FINITE-DIFFERENCE SCHEME, NUMERICAL-SOLUTION, ELEMENT-METHOD
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

© 2022, The Author(s), under exclusive licence to Islamic Azad University.This work proposes a finite element method emphasizing with quartic-trigonometric basis functions for finding the numerical solution of nonlinear Burgers’ equation. The computational scheme is constructed by a discretized space-time hybrid approach using B-spline functions. This methodology produces a system of time-dependent differential equations which is integrated by finite elements technique. The experimental cases including graphical patterns of each wave interaction are simulated by the current computational algorithm. In addition, the method establishes the capacity to provide highly efficient solutions with relative ease of computation. Investigation of the stability analysis shows that the current computational method serves an unconditional stable numerical scheme.