A Positivity-preserving Numerical Scheme for a Nonlinear Fourth Order Parabolic System

Jüngel, Ansgar; Pinnau, René

A Positivity-preserving Numerical Scheme for a Nonlinear Fourth Order Parabolic System

Files

preprint_112.pdf(717.51 KB)

Date

2000

Authors

Jüngel, Ansgar

Pinnau, René

Series

Konstanzer Schriften in Mathematik und Informatik; 112

Publication type

Preprint

Abstract

A positivity-preserving numerical scheme for a fourth order nonlinear parabolic system arising in quantum semiconductor modelling is studied. The system is numerically treated by introducing an additional nonlinear potential and a subsequent semidiscretization in time. The resulting sequence of nonlinear second order elliptic systems admits at each time level strictly positive solutions, which is proved by an exponential transformation of variables. The stability of the scheme is shown and convergence is proved in one space dimension. The results extend under additional assumptions to the multi-dimensional case. Assuming enough regularity on the solution the rate of convergence proves to be optimal. Numerical results concerning the switching behaviour of a resonant tunneling diode are presented.

Subject (DDC)

004 Computer Science

Cite This

ISO 690

JÜNGEL, Ansgar, René PINNAU, 2000. A Positivity-preserving Numerical Scheme for a Nonlinear Fourth Order Parabolic System

BibTex

@unpublished{Jungel2000Posit-6224,
  year={2000},
  title={A Positivity-preserving Numerical Scheme for a Nonlinear Fourth Order Parabolic System},
  author={Jüngel, Ansgar and Pinnau, René}
}

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