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

Authors

Suanrong Chen, University of Southern MississippiFollow
Jiu Ding, University of Southern MississippiFollow

Document Type

Article

Publication Date

10-15-2012

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

Let S: [0,1] → [0,1] be a nonsingular transformation such that the corresponding Frobenius–Perron operator P_S: L¹ (0,1) → L¹ (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.

Publication Title

Applied Mathematics and Computation

Volume

219

Issue

3

First Page

1047

Last Page

1052

Recommended Citation

Chen, S., Ding, J. (2012). A Piecewise Constant Method for Frobenius-Perron Operators via Delta Function Approximations. Applied Mathematics and Computation, 219(3), 1047-1052.
Available at: https://aquila.usm.edu/fac_pubs/7594