Re: [R] LSODA not accurate when RK4 is; what's going on?

From: Ravi Varadhan <rvaradhan_at_jhmi.edu>
Date: Thu, 10 Apr 2008 10:18:51 -0400

John,

I should also mention that by looking at the R source for lsoda() you can see that the default values for "atol" and "rtol" are 1.e-06. This should have been mentioned in the help file, but is not.

Another approach to solving your problem is to restrict "hmax", the maximum steplength.

s4 <- lsoda(y=sqrt(pi/2), times=t4, func=fn, parms=0, hmax=0.001)

plot(s4, type="l")

Best,
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  



-----Original Message-----
From: r-help-bounces_at_r-project.org [mailto:r-help-bounces_at_r-project.org] On Behalf Of John Tillinghast
Sent: Wednesday, April 09, 2008 7:18 PM
To: r-help_at_r-project.org
Subject: [R] LSODA not accurate when RK4 is; what's going on?

I'm solving the differential equation dy/dx = xy-1 with y(0) = sqrt(pi/2). This can be used in computing the tail of the normal distribution. (The actual solution is y(x) = exp(x^2/2) * Integral_x_inf {exp(-t^2/2) dt} = Integral_0_inf {exp (-xt - t^2/2) dt}. For large x, y ~ 1/x, starting around x~2.)

I'm testing both lsoda and rk4 from the package odesolve. rk4 is accurate using step length 10^-2 and probably would be with even larger steps.

lsoda is pretty accurate out to about x=4, then starts acting strangely. For step length 10^-3, y suddenly starts to increase after 4, when it should be strictly decreasing. For step length 10^-4, y instead turns down and start dropping precipitously.

Any ideas why lsoda would go off the rails when rk4 does so well? I will soon be using R to solve more complicated systems of ODEs which I don't understand as well, so I want to know when it can mislead me.

Code:
t4 <- seq(0, 5, by=.0001)
> fn

function(t,y,parms=0){return(list(t*y-1))} s4 <- lsoda(sqrt(pi/2), t4, fn, 0)

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https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Thu 10 Apr 2008 - 14:28:23 GMT

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