An Alternating Direction Implicit Finite Element Galerkin Method for the Linear Schrödinger Equation
An Alternating Direction Implicit Finite Element Galerkin Method for the Linear Schrödinger Equation
Abstract We formulate and analyze a fully-discrete approximate solution of the linear Schrödinger equation on the unit square written as a Schrödinger-type system. The finite element Galerkin method is used for the spatial discretization, and the time-stepping is done with an alternating direction implicit extrapolated Crank-Nicolson method. We demonstrate the …