R help - Nov 2010 - non-linear fourth-order differential equations

I need to solve a system of non-linear fourth-order differential
equations. Is there a command which solves this system?

Thanks in advance.

Hi Yanika,

Please try ?uniroot and ?ployroot

f <- function(x) x^4-16
uniroot(f, lower= -3, upper=0)
polyroot(c(-16,0,0,0,1))

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Hi Yanika,

Depending on whether your problem is an initial value problem or a
boundary value problem, you can find solution methods in R-packages
deSolve (IVP) and bvpSolve (BVP).

The solvers in deSolve only solve differential equations written in
first-order form; bvpSolve can handle higher-order DEs.

For use in deSolve, you need to rewrite the 4th order DE as a set of 4
first-order equations:
d''''y /dt = f(t,y) then becomes:
dy1 = y2; dy2 = y3; dy3 = y4; dy4 = f(t,y)

Hope this helps,


Karline

Message: 32
Date: Sun, 28 Nov 2010 22:47:59 +0100
From: Yanika Borg <akinay.b at gmail.com>
To: r-help at r-project.org
Subject: [R] non-linear fourth-order differential equations
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	<AANLkTimhoquHfSnjxr_n4zttrpPp4Ohw++URA6APxUk+ at mail.gmail.com>
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I need to solve a system of non-linear fourth-order differential
equations. Is there a command which solves this system?

Thanks in advance.

Hi Yanika,

more information about deSolve (books, papers, tutorials) can be found 
on the deSolve homepage:

http://desolve.r-forge.r-project.org

and, of course, in the package documentations. If you need further help 
from the list, please provide a short reproducible example.

Thomas Petzoldt


-- 
Dr. Thomas Petzoldt
Limnology and Ecological Modelling

Technische Universitaet Dresden
Fakulty of Forest, Geo and Hydro Sciences
Institute of Hydrobiology
01062 Dresden, Germany
E-Mail: thomas.petzoldt at tu-dresden.de
http://tu-dresden.de/Members/thomas.petzoldt