[R] How to solve differential equations with a delay (time lag)?

[Setzer.Woodrow at epamail.epa.gov]

lsoda does not solve delay differential equations, which is what you
need to be able to do.  A quick search on netlib (netlib.org) turned up
one match for "delay differential equations": ode/ddverk.f, which might
help (though not in R).

R. Woodrow Setzer, Ph. D.
National Center for Computational Toxicology
US Environmental Protection Agency
Mail Drop B205-01/US EPA/RTP, NC 27711
Ph: (919) 541-0128    Fax: (919) 541-1194


                                                                        
             Ravi Varadhan                                              
             <rvaradhan at jhmi.                                           
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                                      [R] How to solve differential     
             11/29/2006 04:44         equations with a delay (time      
             PM                       lag)?                             
                                                                        
                                                                        
                                                                        
                                                                        
                                                                        
                                                                        




Hi,



I would like to solve a system of coupled ordinary differential
equations,
where there is a delay (time lag) term.  I would like to use the "lsoda"
function "odesolve" package.  However, I am not sure how to specify the
delay term using the syntax allowed by odesolve.

Here is an example of the kind of problem that I am trying to solve:



> library(odesolve)



yprime <- function(t, y, p) {  # this function

yd1 <- p["k1"] *(t <= p["T"]) - p["k2"] * y[2]

yd2 <- p["k3"] * y[1](t - p["delay"]) - p["k4"] * y[2]  # this is not
syntactically valid, but it is what I would like to do

list(c(yd1,yd2))

}



times <- seq(0,30,by=0.1)

y0 <- c(0,0)

parms <- c(k1=0.7, k2=0.5, k3=0.2, k4=0.8, T=10, delay=5)



Is there a way to incorporate delay in odesolve?



Any hints would be much appreciated.



Ravi.

----------------------------------------------------------------------------

-------

Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu

Webpage:
http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html



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