Difference Methods for Stiff Delay Differential Equations

Roth, Mitchell Godfrey

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Description

Title

Difference Methods for Stiff Delay Differential Equations

Author(s)

Roth, Mitchell Godfrey

Issue Date

1981

Department of Study

Computer Science

Discipline

Computer Science

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

Mathematics

Language

eng

Abstract

• 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.
• A computer code for stiff delay equations was developed using the stiffly stable backward differentiation formulae (BDF). In a three-way comparison with non-stiff Adam's and Runge-Kutta methods, the BDF method required significantly less computation for stiff problems and only slightly more computation for non-stiff problems.

Graduation Semester

1981

Type of Resource

text

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http://hdl.handle.net/2142/66450

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