PINK NOISE, l/fa NOISE, AND THEIR EFFECT ON SOLUTIONS OF DIFFERENTIAL EQUATIONS

摘要

White noise is a very common way to account for randomness in the inputs to partial differential equations, especially in cases where little is know about those inputs. On the other hand, pink noise, or more generally, colored noise having a power spectrum that decays as l//a, where f denotes the frequency and oc G (0,2] has been found to accurately model many natural, social, economic, and other phenomena. Our goal in this paper is to study, in the context of simple linear and nonlinear two-point boundary-value problems, the effects of modeling random inputs as 1 // a random fields, including the white noise (oc = 0), pink noise (oc = 1), and brown noise (oc = 2) cases. We show how such random fields can be approximated so that they can be used in computer simulations. We then show that the solutions of the differential equations exhibit a strong dependence on oc, indicating that further examination of how randomness in partial differential equations is modeled and simulated is warranted.