Numerical solutions of the KdV equation using B-spline functions

Lakestanı M.

Iranian Journal of Science and Technology, Transaction A: Science, cilt.41, sa.2, ss.409-417, 2017 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 2
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1007/s40995-017-0260-7
  • Dergi Adı: Iranian Journal of Science and Technology, Transaction A: Science
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.409-417
  • Anahtar Kelimeler: B-spline function, Collocation method, De Vries equation, Korteweg, Stability
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

A numerical technique based on the finite difference and collocation methods is presented for the solution of Korteweg–de Vries (KdV) equation. The integration relations between any two families of B-spline functions are presented and are utilized to reduce the solution of KdV equation to the solution of linear algebraic equations. Numerical simulations for three test examples have been demonstrated to validate the technique proposed in the current paper. It is found that the simulating results are in good agreement with the exact solutions.