A stable numerical method for multidimensional time fractional Schrödinger equations

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• 作者：Betul Hicdurmaz^a ; ^{betul.hicdurmaz@medeniyet.edu.tr" class="auth_mail" title="E-mail the corresponding author} ; Allaberen Ashyralyev^b
• 关键词：Time fractional Schr&ouml ; dinger equation ; Finite difference scheme ; Stability ; Two-dimensional Schr&ouml ; dinger equation
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：72
• 期：6
• 页码：1703-1713
• 全文大小：668 K

文摘

In this paper, the stability analysis is presented for a first order difference scheme applied to a nonhomogeneous time fractional Schrödinger 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 Schrödinger differential equations. Theoretical findings are validated by numerical experiments on one and two-dimensional time fractional Schrödinger differential equations.