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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-21 16:01 |
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Conference: Bucharest University Faculty of Physics 2008 Meeting
Section: Electricity and Biophysics
Title:
Numerically integrating DDE: Difficulties commonly encountered
Authors:
C.M.Niculae and M. Niculae
Affiliation:
Faculty of Physics, University of Bucharest, Bucharest-Magurele - P.O. Box MG11, 077125, Romania
E-mail
cniculae@gmail.com
Keywords:
Delay Differential Equations, Numerical methods, Runge-Kutta
Abstract:
Even Delay Differential Equations (DDEs) have been used for many years in control theory and only recently have been applied to biological models, there are some commonly encounter difficulties that a newcomer have to surpass in dealing with them.
As an illustration of these difficulties the following test problem was built. Let consider the DDE given by
y`(t)=a*y(t)+b*y(t-T), (1)
where a, b, and T are given constants. Let consider as initial condition the function
Y(t)=exp(G*t)*cos(W*t), for t<=0, where G and W are given constants. Our task is to integrate numerically this equation for t>0.
In our analysis we compare the numerical results given by four Runge-Kutta methods. All of them use a third order interpolating polynomial. Also we discuss the stability of numerical methods used. Some considerations concerning the characteristic equation of equation (1) are given.
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