Preprint 1996-026

Convergence of Implicit Finite Difference Methods applied to Nonlinear Mixed Systems

Abstract: A new technique to prove convergence of finite difference methods applied to nonlinear PDEs arising in computational fluid dynamics is presented. The underlying systems may be hyperbolic, parabolic or of mixed type like the Navier--Stokes equations. Implicit finite difference methods are analyzed. The essential idea leading to success is the introduction of a pilot function, that is highly attractive to the numerical approximation and converges itself to the solution of the underlying system.

Paper:

Available as PostScript

Title:

Convergence of Implicit Finite Difference Methods applied to Nonlinear Mixed Systems

Author(s):

H. J. Schroll, mailto:schroll@igpm.rwth-aachen.de

Publishing information:

SIAM J. Num. Anal. 33(3), 1996, pp 997-1013.

Submitted by:

mailto:schroll@igpm.rwth-aachen.de August 26 1996.