Title

A Piecewise Constant Method for Frobenius-Perron Operators via Delta Function Approximations

Document Type

Article

Publication Date

10-15-2012

Department

Mathematics

Abstract

Let S : [0, 1] -> [0, 1] be a nonsingular transformation such that the corresponding Frobenius-Perron operator P-S : L-1(0, 1) -> L-1(0, 1) has a stationary density f*. We develop a piecewise constant method for the numerical computation of f*, based on the approximation of Dirac's delta function via pulse functions. We show that the numerical scheme out of this new approach is exactly the classic Ulam's method. Numerical results are given for several one dimensional test mappings. (C) 2012 Elsevier Inc. All rights reserved.

Publication Title

Applied Mathematics and Computation

Volume

219

Issue

3

First Page

1047

Last Page

1052