EXTENDED B-SPLINE COLLOCATION METHOD FOR KDV-BURGERS EQUATION

Hepson Ö., Korkmaz A., Dag İ.

TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, cilt.9, sa.2, ss.267-278, 2019 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 2
  • Basım Tarihi: 2019
  • Dergi Adı: TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.267-278
  • Anahtar Kelimeler: KdV-Burgers Equation, Extended cubic B-spline, collocation, motion of waves, NUMERICAL-SOLUTION, WAVE SOLUTIONS, EXPLICIT
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

The extended form of the classical polynomial cubic B-spline function is used to set up a collocation method for some initial boundary value problems derived for the Korteweg-de Vries-Burgers equation. Having nonexistence of third order derivatives of the cubic B-splines forces us to reduce the order of the term u(xxx) to give a coupled system of equations. The space discretization of this system is accomplished by the collocation method following the time discretization with Crank-Nicolson method. Two initial boundary value problems, one having analytical solution and the other is set up with a non analytical initial condition, have been simulated by the proposed method.