A family of conservative finite difference schemes for the dynamical von Karman plate equations

Abstract

Numerical methods for nonlinear plate dynamics play an important role across many disciplines. In this article, the focus is on numerical stability for numerical methods for the von Karman system, through the use of energy-conserving methods. It is shown that one may take advantage of structure particular to the system to construct numerical methods, which are provably numerically stable, and for which computer implementation is simplified. Numerical results are presented. © 2007 Wiley Periodicals, Inc.