A New Perspective on The Numerical Solution for Fractional Klein Gordon Equation

Karaagac B., UÇAR Y., YAĞMURLU N. M., ESEN A.

JOURNAL OF POLYTECHNIC-POLITEKNIK DERGISI, cilt.22, sa.2, ss.443-451, 2019 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.2339/politeknik.428986
  • Dergi Adı: JOURNAL OF POLYTECHNIC-POLITEKNIK DERGISI
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.443-451
  • Anahtar Kelimeler: Finite element method, collocation, Fractional Klein Gordon equation, Caputo derivative, PARTIAL-DIFFERENTIAL-EQUATIONS, TIME, SCHEME
  • İnönü Üniversitesi Adresli: Evet

Özet

In the present manuscript, a new numerical scheme is presented for solving the time fractional nonlinear Klein-Gordon equation. The approximate solutions of the fractional equation are based on cubic B-spline collocation finite element method and L2 algorithm. The fractional derivative in the given equation is handled in terms of Caputo sense. Using the methods, fractional differential equation is converted into algebraic equation system that are appropriate for computer coding. Then, two model problems are considered and their error norms are calculated to demonstrate the reliability and efficiency of the proposed method. The newly calculated error norms show that numerical results are in a good agreement with the exact solutions.