TY - JOUR
T1 - An alternating direction implicit finite element Galerkin method for the linear Schrödinger equation
AU - Khebchareon, Morrakot
AU - Pani, Amiya K.
AU - Fairweather, Graeme
AU - Fernandes, Ryan I.
N1 - Publisher Copyright:
© 2024, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2024
Y1 - 2024
N2 - 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 existence and uniqueness of the approximation, and prove that the scheme is of optimal accuracy in the L2, H1 and L∞ norms in space and second-order accurate in time. Numerical results are presented which support the theory.
AB - 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 existence and uniqueness of the approximation, and prove that the scheme is of optimal accuracy in the L2, H1 and L∞ norms in space and second-order accurate in time. Numerical results are presented which support the theory.
KW - Alternating direction implicit method
KW - Extrapolated Crank-Nicolson method
KW - Finite element Galerkin method
KW - Linear Schrödinger equation
KW - Numerical experiments
KW - Optimal-order convergence
KW - Schrödinger-type systems
UR - http://www.scopus.com/inward/record.url?scp=85182830744&partnerID=8YFLogxK
U2 - 10.1007/s11075-023-01740-5
DO - 10.1007/s11075-023-01740-5
M3 - Article
AN - SCOPUS:85182830744
SN - 1017-1398
JO - Numerical Algorithms
JF - Numerical Algorithms
ER -