An alternating direction implicit finite element Galerkin method for the linear Schrödinger equation.

Autor:	Khebchareon, Morrakot, Pani, Amiya K., Fairweather, Graeme, Fernandes, Ryan I.
Předmět:	FINITE element method CRANK-nicolson method SCHRODINGER equation LINEAR equations
Zdroj:	Numerical Algorithms; Nov2024, Vol. 97 Issue 3, p1039-1066, 28p
Abstrakt:	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 L 2 , H 1 and L ∞ norms in space and second-order accurate in time. Numerical results are presented which support the theory. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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