A multirate ordinary differential equation integrator /

Originally presented as the author's thesis, University of Illinois at Urbana-Champaign.

An efficient numerical method for highly oscillatory ordinary differential equations /

"Supported in part by the Department of Energy under contract ENERGY/EY-76-S-02-2383, and submitted in partial fulfillment of the requirements of the Graduate College for the degree of doctor of philosophy."

Study of stability for non-linear ordinary differential equations.

"C00-1469-0118."

A user's view of solving stiff ordinary differential equations /

"COO-2383-0036."

Automatic detection and treatment of oscillatory and/or stiff ordinary differential equations /

"Presented at the Differential Equation Workshop, Center for Interdisciplinary Research (Zif), University of Bielefeld, West Germany, April 21, 1980."

Hybrid methods for initial value problems in ordinary differential equations /

At head of title: COO-415-1012.

Automatic multirate methods for ordinary differential equations /

"UILU-ENG 80 1701."

Optimal stiffly stable methods for ordinary differential equations,

"COO-1469-0164."

Asymptotic estimation of errors and derivatives for the numerical solution of ordinary differential equations,

"Supported in part by contract US AEC AT(11-1)2383."

Stability of variable-step methods for ordinary differential equations /

Bibliography: leaf 11.

A comparison of techniques for the numerical integration of ordinary differential equations,

"COO-1469-0082."

The automatic integration package for ordinary differential equations,

"COO-1469-0103."

Numerical simulation of stochastic ordinary differential equations in biomathematical modelling

In this work we discuss the effects of white and coloured noise perturbations on the parameters of a mathematical model of bacteriophage infection introduced by Beretta and Kuang in [Math. Biosc. 149 (1998) 57]. We numerically simulate the strong solutions of the resulting systems of stochastic ordinary differential equations (SDEs), with respect to the global error, by means of numerical methods of both Euler-Taylor expansion and stochastic Runge-Kutta type. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved.

A genetic estimation algorithm for parameters of stochastic ordinary differential equations

A generic method for the estimation of parameters for Stochastic Ordinary Differential Equations (SODEs) is introduced and developed. This algorithm, called the GePERs method, utilises a genetic optimisation algorithm to minimise a stochastic objective function based on the Kolmogorov-Smirnov statistic. Numerical simulations are utilised to form the KS statistic. Further, the examination of some of the factors that improve the precision of the estimates is conducted. This method is used to estimate parameters of diffusion equations and jump-diffusion equations. It is also applied to the problem of model selection for the Queensland electricity market. (C) 2003 Elsevier B.V. All rights reserved.