Hello Sheehan,
I get a failure with the following example, do you have an idea about the
why ?:
*# solves u = phi²*sinh(u)-2u'/(x+gamma) , u'(a)=-xi, u'(R)=0*
*a= 3.514457e-07*
*R= 7.60773e-07*
*x=Fun(identity, Interval(a,R))*
*d=x.domain*
*B=neumann(d)*
*D=diff(d)*
*# Solves Lu + g(u) == 0*
Hi Stephane,
It's a problem of accurate initial guess. I got a good initial guess
by doing a homotopy down from phi=1000.The solution should be
Thank you for the explanations. Reading your papers is on my LOTTD. Some pub
for you here http://stats.stackexchange.com/a/104290/8402 ;)
Hello,
I'd like to solve this equation with Neumann boundary conditions. My code
below does not work. Am I doing something bad or is it a failure of the
Newton algorithm ?
*# solves u = (exp(u)-exp(-u))-2u'/(x+1) , u'(0)=-1, u(1)=0*
*x=Fun(identity, Interval(0.,1.))*
*d=x.domain*
Hi,
You didn’t quite get the Newton iteration right: if you want to solve
B u + [1,0] = 0
L u + g(u) = 0
then Newton iteration becomes
u = u - [B, L + g’(u)]\[B u + [1,0], L u + g(u)]
i.e., your bc right hand side is not right. Below is the corrected
Ok, I understand. It works and it is really awesome. Thank you !
Le samedi 21 juin 2014 12:17:22 UTC+2, Sheehan Olver a écrit :
Hi,
You didn’t quite get the Newton iteration right: if you want to solve
B u + [1,0] = 0
L u + g(u) = 0
then Newton iteration becomes
u = u - [B, L +
Thanks!
I'm interested to know if the ultraspherical spectral approach has any clear
advantages over spectral collocation for nonlinear odes. (For linear odes the
advantages are clear.)
So if you find the code better than expected please let me know. It's a bit
buggy and unoptimized, so
Sorry but I really don't understand you first sentence.
About the code, I will possibly experiment it during the next days or
weeks, and I'll send you some feedback.
Thank you again for this library and your help.
- Stéphane
Le samedi 21 juin 2014 14:24:03 UTC+2, Sheehan Olver a écrit :
Sorry for the confusion, the numerics for linear ode solving in ApproxFun is
built on the ultra spherical spectral method by myself and Alex Townsend:
A fast and well-conditioned spectral method, SIAM Review, 55: 462–489
http://epubs.siam.org/doi/abs/10.1137/120865458
It's different from
Btw I fixed a bug so now
norm((exp(u)-exp(-u))-2diff(u)./(x+1)-diff(u,2))
returns 0.0 (not sure why not machine eps…)
On 21 Jun 2014, at 10:58 pm, 'Stéphane Laurent' via julia-users
julia-users@googlegroups.com wrote:
Sorry but I really don't understand you first
Thank you, it works !!
NB: I'm Stéphane and not Stéphanie :-)
Le vendredi 20 juin 2014 00:13:08 UTC+2, Sheehan Olver a écrit :
Hi Stephanie,
Are you on the latest GitHub version? You can get on it with
Pkg.checkout(ApproxFun)
Sent from my iPad
On 20 Jun 2014, at 3:19 am, 'Stéphane
Cool! Let me know if you want any functionality added to make it useful.
Sent from my iPhone
On Jun 20, 2014, at 11:11 PM, 'Stéphane Laurent' via julia-users
julia-users@googlegroups.com wrote:
Thank you, it works !!
NB: I'm Stéphane and not Stéphanie :-)
Le vendredi 20 juin 2014
Hello Sheehan,
I get this error when I run your code:
julia for k=1:5
u=u-[B,L+gp(u)]\[0.,0.,L*u+g(u)-1.];
end
ERROR: Reducing over an empty array is not allowed.
in _mapreduce at reduce.jl:151
in mapreduce at reduce.jl:173
in old_addentries! at
Hi Stephanie,
Are you on the latest GitHub version? You can get on it with
Pkg.checkout(ApproxFun)
Sent from my iPad
On 20 Jun 2014, at 3:19 am, 'Stéphane Laurent' via julia-users
julia-users@googlegroups.com wrote:
Hello Sheehan,
I get this error when I run your code:
julia for
Hi Stèphane,
Nonlinear is not built in, but it’s easy enough to do by hand with
Newton iteration in function space. Let me know if there is any confusion with
the code below. I suppose I could just add a “nonlinsolve” routine that
bundles this up.
(I am on the latest
I tagged a new release for ApproxFun
(https://github.com/dlfivefifty/ApproxFun) with major new features that
might interest people. Below are ODE solving and random number sampling
examples, find more in ApproxFun/examples. The code is meant as alpha
quality, so don't expect too much beyond
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