Ok, thank you. I think I have a way to find a valuable guess in my problem
Le vendredi 11 juillet 2014 05:48:42 UTC+2, Sheehan Olver a écrit :
>
> 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
>
>
> IFun{Float64,Interval{Float64}}([17.0558,-9.62248e-7,2.40562e-7,-5.76944e-14,4.82252e-15],Interval{Float64}(3.514457e-7,7.60773e-7))
>
>
> If you replace your initial guess with the this solution it should work,
> also as you perturb your parameters.
>
> (These subtleties are why I'm hesitant to build in a nonlinear solver.)
>
> Hope that helps!
>
> Sheehan
>
>
>
>
> On 10 Jul 2014, at 8:21 pm, 'Stéphane Laurent' via julia-users <
> [email protected] <javascript:>> wrote:
>
> 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*
> *phi=1.341211*
> *gamma=0.8585931*
> *L = D^2 + 2/(x.+gamma)*D*
> *g = u -> -phi^2*(exp(u)-exp(-u))/2; gp = u -> -phi^2*(exp(u)+exp(-u))/2*
>
> *u=0.x #initial guess *
> *xi=9.403218*
> *for k=1:5*
> * u=u-[B,L+gp(u)]\[diff(u)[a]+xi,diff(u)[R],L*u+g(u)];*
> *end*
>
>
> *julia> u*
> *IFun{Float64,Interval{Float64}}([NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN
> …
>
> NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN],Interval{Float64}(3.514457e-7,7.60773e-7))*
>
>
>
>
>
>
