Numerical Solution of Fractional Order Burgers' Equation with Dirichlet and Neumann Boundary Conditions by Reproducing Kernel Method


Saldır O., Sakar M. G. , Erdoğan F.

FRACTAL AND FRACTIONAL, vol.4, no.2, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 4 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.3390/fractalfract4020027
  • Journal Name: FRACTAL AND FRACTIONAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Burgers' equation, reproducing kernel method, error estimate, Dirichlet and Neumann boundary conditions, Caputo derivative, FINITE-DIFFERENCE, ELEMENT APPROACH, APPROXIMATION, DERIVATIVES, ALGORITHM, SYSTEMS, FLUID, FLOW
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this research, obtaining of approximate solution for fractional-order Burgers' equation will be presented in reproducing kernel Hilbert space (RKHS). Some special reproducing kernel spaces are identified according to inner products and norms. Then an iterative approach is constructed by using kernel functions. The convergence of this approach and its error estimates are given. The numerical algorithm of the method is presented. Furthermore, numerical outcomes are shown with tables and graphics for some examples. These outcomes demonstrate that the proposed method is convenient and effective.