Optimal Error Estimates in Numerical Solution of Time Fractional Schrödinger Equations on Unbounded Domains

Abstract

The artificial boundary method is used to reformulate the time fractional Schrödinger equation on the real line as a bounded problem with exact artificial boundary conditions. The problem appeared is solved by a numerical method employing the L1-formula for the Caputo derivative and finite differences for spatial derivatives. The convergence of the method studied and optimal error estimates in a special metric are obtained. The technique developed here can be also applied to study the convergence of approximation methods for standard Schrödinger equation.