An iterative approximation for time-fractional Cahn-Allen equation with reproducing kernel method


Sakar M. G., Saldır O., Erdoğan F.

COMPUTATIONAL & APPLIED MATHEMATICS, vol.37, no.5, pp.5951-5964, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 5
  • Publication Date: 2018
  • Doi Number: 10.1007/s40314-018-0672-9
  • Journal Name: COMPUTATIONAL & APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.5951-5964
  • Keywords: Caputo derivative, Cahn-Allen equation, Reproducing kernel method, Convergence, 35R11, 46E22
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this article, we construct a novel iterative approach that depends on reproducing kernel method for Cahn-Allen equation with Caputo derivative. Representation of solution and convergence analysis are presented theoretically. Numerical results are given as tables and graphics with intent to show efficiency and power of method. The results demonstrate that approximate solution uniformly converges to exact solution for Cahn-Allen equation with fractional derivative.