In this review article we discuss different techniques to solve numerically the time-dependent
Schrödinger equation on unbounded domains. We present in detail the most recent …

The modelling of sound propagation in the ocean by the solution of mode parabolic
equations is discussed. Mode parabolic equations can be obtained as the one-way …

In this work we improve the algorithm of Han and Wu [SIAM J. Numer. Anal. 41 (2003), 2081–
2095] for American Options with respect to stability, accuracy and order of computational …

In this paper, we introduce artificial boundary conditions for the linearized Green--Naghdi
system of equations. The derivation of such continuous (respectively, discrete) boundary …

We consider various approximations of artificial boundary conditions for linearized Benjamin–
Bona–Mahony BBM equation. Continuous (respectively discrete) artificial boundary …

We propose transparent boundary conditions (TBCs) for the time–dependent Schrödinger
equation on a circular computational domain. First we derive the two–dimensional discrete …

In this work we deal with the numerical solution of some problems of air pollution. Since the
problems are posed on unbounded domains we have to introduce artificial boundaries to …

In this paper, we consider artificial boundary conditions for the linearized mixed Korteweg–
de Vries (KDV) and Benjamin–Bona–Mahoney (BBM) equation which models water waves …

In this work we improve and extend a technique named recursive doubling procedure
developed by Yuan and Lu [J. Lightwave Technology 25 (2007), 3649-3656] for solving …

This paper deals with absorbing boundary conditions for hyperbolic systems in one and two
space dimensions. We prove the strict well–posedness of the resulting initial boundary value …