On the numerical solution of fractional Schrödinger differential equations with the Dirichlet condition

Abstract

The first and second orders of accuracy difference schemes for the mixed problem for the multidimensional fractional Schrödinger differential equation with dependent coefficients are considered. Stability estimates for solutions of these difference schemes are obtained. Numerical methods are proposed for solving the one-dimensional fractional Schrödinger differential equation with Dirichlet condition in the space variable.

Keywords:

• difference scheme
• fractional Schrödinger differential equation
• Dirichlet condition
• fractional differential equation
• stability

2000 AMS Subject Classifications::

• 65M06
• 35R11