Difference Methods for Stiff Delay Differential Equations

Delay differential equations of the form y'(t) = f(y(t), z(t)), where z(t) = {y(,1)((alpha)(,1)(y(t))),..., y(,n)((alpha)(,n)(y(t)))}('T) and (alpha)(,i)(y(t)) (LESSTHEQ) t arise in many scientific and engineering fields when transport lags and propagation times are physically significant in a dynamic process. Difference methods for approximating the solutions of stiff delay systems require special stability properties that are generalizations of those employed for stiff ordinary differential equations. Using the model equation (y'(t) = py(t) + qy(t-1), with complex p and q, the definitions of A-stability, (A((alpha))-stability, and stiff stability have been generalized to delay equations. For linear multistep difference formulas, these properties extend directly from ordinary to delay equations. This is not true for implicit Runge-Kutta methods, as illustrated by the mid-point formula, which is A-stable for ordinary equations, but not for delay equations.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Roth, Mitchell Godfrey

• Mathematics

Language dc:language

eng

Identifier

(UMI)AAI8114471

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/66450