A novel iterative solution for time-fractional Boussinesq equation by reproducing kernel method

Sakar M. G., Saldır O.

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, vol.64, no.1-2, pp.227-254, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 64 Issue: 1-2
  • Publication Date: 2020
  • Doi Number: 10.1007/s12190-020-01353-4
  • Journal Name: JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Aerospace Database, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.227-254
  • Keywords: Reproducing kernel method, Boussinesq equation, Fractional order, Convergence, PARTIAL INTEGRODIFFERENTIAL EQUATIONS, NUMERICAL-SOLUTIONS, HILBERT-SPACE, ALGORITHM, SUBJECT
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this study, iterative reproducing kernel method (RKM) will be applied in order to observe the effect of the method on numerical solutions of fractional order Boussinesq equation. Hilbert spaces and their kernel functions, linear operators and base functions which are necessary to obtain the reproducing kernel function are clearly explained. Iterative solution is constituted in a serial form by using reproducing kernel function. Then convergence of RKM solution is shown with lemma and theorem. Two problems, "good" Boussinesq and generalized Boussinesq equations, are examined by using RKM for different fractional values. Results are presented with tables and graphics.