A note on discretization of nonlinear differential equations.
An important issue when integrating nonlinear differential equations on a digital computer is the choice of the time increment or step size. For example, it is known that if this quantity is not sufficiently short, spurious chaotic motions may be induced when integrating a system using several of the well-known methods available in the literature. In this paper, a new approach to discretize differential equations is analyzed in light of computational chaos. It will be shown that the fixed points of the continuous system are preserved under the new discretization approach and that the spurious fixed points generated by higher order approximations depend upon the increment parameter. (c) 2002 American Institute of Physics.
Mendes
Eduardo M. A. M.
EM
Department of Government, University of Texas at Austin, Burdine Hall 536D, Austin, Texas 78712-1087.
Billings
S. A.
SA