Solutions of the fractional combined KdV–mKdV equation with collocation method using radial basis function and their geometrical obstructions

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KAYA D., Gülbahar S., Yokuş A., Gülbahar M.

Advances in Difference Equations, cilt.2018, sa.1, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2018 Sayı: 1
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1186/s13662-018-1531-0
  • Dergi Adı: Advances in Difference Equations
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Collocation method, Fractional combined Korteweg-de Vries and modified Korteweg-de Vries equation, Lorentz-Minkowski space
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

The exact solution of fractional combined Korteweg-de Vries and modified Korteweg-de Vries (KdV–mKdV) equation is obtained by using the (1 / G′) expansion method. To investigate a geometrical surface of the exact solution, we choose γ= 1. The collocation method is applied to the fractional combined KdV–mKdV equation with the help of radial basis for 0 OpenSPiltSPi γOpenSPiltSPi 1. L2 and L∞ error norms are computed with the Mathematica program. Stability is investigated by the Von-Neumann analysis. Instable numerical solutions are obtained as the number of node points increases. It is shown that the reason for this situation is that the exact solution contains some degenerate points in the Lorentz–Minkowski space.