Date:

Monday, March 31, 2008,
11:00 am - 12:00 pm.

Place:

Mathematics Conference Room 626, UCD Building, 1250 14th St., Denver.

Speaker:

Gilles Zérah.

Affiliation:

CEA-Bruyères (Commissariat à l'Energie Atomique, Centre d'Etudes de Bruyères-le-Châtel), France.

Title:

An $L^\infty$ error bound for the Feynman splitting.

Abstract:

The Feynman (or Feynman-Strang-Marchuk) splitting is a widely used method to compute the exponential of an operator of the form $e^{t(A+B)}$ by $e^{t/2B} e^{tA} e^{t/2B}$. When A and B are bounded, and error can easily be obtained through the power series of the exponential. When A or B are unbounded, this is more delicate, and we here consider the case where $A=-\Delta /2 $ and B is bounded. (The Schroedinger operator.) In this case, errors bound have been obtained in the p,p norm (that is from $L^p$ to $L^p$) (see e.g. [JaLu99]) and we here present [LRZé07] an error bound in the $1, \infty$ norm and show why we need them for practical physical applications.

References:

[JaLu99] Error Bounds For Exponential Operator Splitting (1999) Jahnke T., Lubich C., BIT Numerical Mathematics
[LRZé07] Convergence stability and estimator in orbital free electronic structure calculation on a grid at finite temperature (2007), Le Roux S., Zérah G., Journal of Computational Physics