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We propose a way to efficiently treat the well-known transparent boundary conditions for the SchrÃ¶dinger equation. Our approach is based on two ideas: to write out a discrete transparent boundaryâ€¦ (More)

This paper is concerned with transparent boundary conditions for the one dimensional timeâ€“dependent SchrÃ¶dinger equation. They are used to restrict the original PDE problem that is posed on anâ€¦ (More)

- Matthias J. Ehrhardt, Kris Thielemans, +4 authors Simon R. Arridge
- 2014

Recent advances in technology have enabled the combination of positron emission tomography (PET) with magnetic resonance imaging (MRI). These PET-MRI scanners simultaneously acquire functional PETâ€¦ (More)

In this review article we discuss different techniques to solve numerically the time-dependent SchrÃ¶dinger equation on unbounded domains. We present in detail the most recent approaches and describeâ€¦ (More)

- Daniel Heubes, Andreas Bartel, Matthias J. Ehrhardt
- J. Computational Applied Mathematics
- 2014

For numerically solving fluid dynamics problems efficiently one is often facing the problem that one has to confine the computational domain to a small domain of interest introducing so-calledâ€¦ (More)

- Quang A. Dang, Matthias J. Ehrhardt
- Mathematical and Computer Modelling
- 2006

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 confine theâ€¦ (More)

Abstract. Environmental problems are becoming more and more important for our world and their importance will even increase in the future. High pollution of air, water and soil may cause damage toâ€¦ (More)

- Andrea Zisowsky, Matthias J. Ehrhardt
- Mathematical and Computer Modelling
- 2008

In this work we construct and analyze discrete artificial boundary conditions (ABCs) for different finite difference schemes to solve nonlinear SchrÃ¶dinger equations. These new discrete boundaryâ€¦ (More)

- Julia Ankudinova, Matthias J. Ehrhardt
- Computers & Mathematics with Applications
- 2008

Nonlinear Blackâ€“Scholes equations have been increasingly attracting interest over the last two decades, since they provide more accurate values by taking into account more realistic assumptions, suchâ€¦ (More)

Transparent boundary conditions (TBCs) are an important tool for the truncation of the computational domain in order to compute solutions on an unbounded domain. In this work we want to show how theâ€¦ (More)