5,367 research outputs found
Mixed-type functional differential equations: A numerical approach
This is a PDF version of a preprint submitted to Elsevier. The definitive version was published in Journal of computational and applied mathematics and is available at www.elsevier.comThis preprint discusses mixed-type functional equations
An algorithm to detect small solutions in linear delay differential equations
This is a PDF version of a preprint submitted to Elsevier. The definitive version was published in the Journal of computational and applied mathematics and is available at www.elsevier.comThis preprint discusses an algorithm that provides a simple reliable mechanism for the detection of small solutions in linear delay differential equations.This article was submitted to the RAE2008 for the University of Chester - Applied Mathematics
Characterising small solutions in delay differential equations through numerical approximations
This paper discusses how the existence of small solutions for delay differential equations can be predicted from the behaviour of the spectrum of the finite dimensional approximations.Manchester Centre for Computational Mathematic
Shape Control for Experimental Continuation
An experimental method has been developed to locate unstable equilibria of
nonlinear structures quasi-statically. The technique involves loading a
structure by application of either a force or a displacement at a main
actuation point, while simultaneously controlling the overall shape using
additional probe points. The method is applied to a shallow arch, and unstable
segments of its equilibrium path are identified experimentally for the first
time. Shape control is a fundamental building block for the experimental---as
opposed to numerical---continuation of nonlinear structures, which will
significantly expand our ability to measure their mechanical response.Comment: Updated Figure 6 experimental results with correct calibration factor
for linear transducer. Updated Figure 6 finite element results with correct
load multiplier for half-model. Updated paper text to reflect these changes.
5 pages, 6 figure
Virtual Testing of Experimental Continuation
We present a critical advance in experimental testing of nonlinear
structures. Traditional quasi-static experimental methods control the
displacement or force at one or more load-introduction points on a structure.
This approach is unable to traverse limit points in the control parameter, as
the immediate equilibrium beyond these points is statically unstable, causing
the structure to snap to another equilibrium. As a result, unstable
equilibria---observed numerically---are yet to be verified experimentally.
Based on previous experimental work, and a virtual testing environment
developed herein, we propose a new experimental continuation method that can
path-follow along unstable equilibria and traverse limit points. To support
these developments, we provide insightful analogies between a fundamental
building block of our technique---shape control---and analysis concepts such as
the principle of virtual work and Galerkin's method. The proposed testing
method will enable the validation of an emerging class of nonlinear structures
that exploit instabilities for novel functionality
Analytical and numerical investigation of mixed-type functional differential equations
NOTICE: this is the authorās version of a work that was accepted for publication in Journal of computational and applied mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of computational and applied mathematics, 234 (2010), doi: 10.1016/j.cam.2010.01.028This journal article is concerned with the approximate solution of a linear non-autonomous functional differential equation, with both advanced and delayed arguments
Solution of a singular integral equation by a split-interval method
The article is available at http://www.math.ualberta.ca/ijnam/Volume-4-2007/No-1-07/2007-01-05.pdf. This article is not available through the Chester Digital RepositoryThis article discusses a new numerical method for the solution of a singular integral equation of Volterra type that has an infinite class of solutions. The split-interval method is discussed and examples demonstrate its effectiveness
Theory and numerics for multi-term periodic delay differential equations, small solutions and their detection
We summarise a theoretical treatment that analyses whether the equation has small solutions. We consider discrete equations that arise when a numerical method with fixed step size is applied to approximate the solution to (ā ) and we develop a corresponding theory. Our results show that small solutions can be detected reliably by the numerical scheme. We conclude with some numerical examples
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