A stable numerical method for multidimensional time fractional Schrodinger equations


HİÇDURMAZ B. , Ashyralyev A.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol.72, no.6, pp.1703-1713, 2016 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 72 Issue: 6
  • Publication Date: 2016
  • Doi Number: 10.1016/j.camwa.2016.07.036
  • Title of Journal : COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Page Numbers: pp.1703-1713
  • Keywords: Time fractional Schrodinger equation, Finite difference scheme, Stability, Two-dimensional Schrodinger equation, COLLOCATION, EXISTENCE

Abstract

In this paper, the stability analysis is presented for a first order difference scheme applied to a nonhomogeneous time fractional Schrodinger differential equation. Based on the z-transform method, stability theorems are proved for the abstract case. The stability results are applied on initial boundary value problems for multidimensional time fractional Schrodinger differential equations. Theoretical findings are validated by numerical experiments on one and two-dimensional time fractional Schrodinger differential equations. (C) 2016 Elsevier Ltd. All rights reserved.