A STABLE SECOND ORDER OF ACCURACY DIFFERENCE SCHEME FOR A FRACTIONAL SCHRODINGER DIFFERENTIAL EQUATION

Ashyralyev A., Hicdurmaz B.

APPLIED AND COMPUTATIONAL MATHEMATICS, vol.17, no.1, pp.10-21, 2018 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 1
  • Publication Date: 2018
  • Journal Name: APPLIED AND COMPUTATIONAL MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded
  • Page Numbers: pp.10-21
  • Keywords: Stability, Fractional Schrodinger Equation, Difference Scheme, Numerical Results, QUANTUM-MECHANICS, TIME, EXISTENCE, ORDER

Abstract

In the present paper, we present and analyze a second order of accuracy difference scheme for solving a fractional Schrodinger differential equation with the fractional derivative in the Riemann Louville sense. A stability analysis is performed on the presented difference scheme. Numerical results confirm the expected convergence rates and illustrate the effectiveness of the method.