Numerical solution of time-fractional Kawahara equation using reproducing kernel method with error estimate

Saldır O., Sakar M. G., Erdoğan F.

COMPUTATIONAL & APPLIED MATHEMATICS, cilt.38, sa.4, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 4
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s40314-019-0979-1
  • Dergi Adı: COMPUTATIONAL & APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Reproducing kernel method, Kawahara equation, Caputo derivative, Convergence, PARTIAL INTEGRODIFFERENTIAL EQUATIONS, HILBERT-SPACE METHOD, STABILITY, ALGORITHM, SUBJECT
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

We present a new approach depending on reproducing kernel method (RKM) for time-fractional Kawahara equation with variable coefficient. This approach consists of obtaining an orthonormal basis function on specific Hilbert spaces. In this regard, some special Hilbert spaces are defined. Kernel functions of these special spaces are given and basis functions are obtained. The approximate solution is attained as serial form. Convergence analysis, error estimation and stability analysis are presented after obtaining the approximate solution. To show the power and effect of the method, two examples are solved and the results are given as table and graphics. The results demonstrate that the presented method is very efficient and convenient for Kawahara equation with fractional order.