Invariant manifolds and global error estimates of numerical integration schemes applied to stiff systems of singular perturbation type -- Part I: RK-methods

1995 ◽  
Vol 70 (2) ◽  
pp. 245-257 ◽  
Author(s):  
K. Nipp ◽  
D. Stoffer
Keyword(s):  
Singular Perturbation ◽  
Numerical Integration ◽  
Error Estimates ◽  
Invariant Manifolds ◽  
Global Error ◽  
Stiff Systems ◽  
Integration Schemes ◽  
Global Error Estimates

scholarly journals Semiclassical Analysis of Discretizations of Schrödinger-type Equations

VLSI Design ◽  
1999 ◽  
Vol 9 (4) ◽  
pp. 397-413 ◽  
Author(s):  
Peter A. Markowich ◽  
Paola Pietra ◽  
Carsten Pohl
Keyword(s):  
Error Estimates ◽  
Global Error ◽  
Wigner Transform ◽  
Semiclassical Analysis ◽  
Planck Constant ◽  
Numerical Examples ◽  
Difference Methods ◽  
Global Error Estimates

We apply Wigner-transform techniques to the analysis of difference methods for Schrödinger-type equations in the case of a small Planck constant. In this way we are able to obtain sharp conditions on the spatial-temporal grid which guarantee convergence for average values of observables as the Planck constant tends to zero. The theory developed in this paper is not based on local and global error estimates and does not depend on whether caustics develop or not.Numerical examples are presented to help interpret the theory.

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