Re: Boundary value problem.


In article <f2hui6$gio$1@xxxxxxxxxxxxxxxxxx>,
Amit Bhatia <abhatia@xxxxxxxxxxxxxxxxx> writes:

Hi,
I am trying to identify the parameters for the following two point
boundary value problem:

y' = f(x,y)=[cos(y(3));sin(y(3));u(y)]
where -1<=u(y)<=1,
u(y)= c1*y(2)-c2*y(1)+c3 OR sign(c1*y-c2*x+c3) , c1,c2,c3 are constants
to be determined.

y(a), y(b) are given to me.

It is a given that there exists smooth differentiable solution to the
problem, but there can be more than one such solutions.


If I solve this problem using bvp4c in matlab, I get the error
"Unable to solve the collocation equations -- a singular Jacobian
encountered"

So apparently my initial guess is not good or there is some other
problem. I was wondering if I should be doing something else or using
something different then this Matlab routine?
The problem is more of parameter estimation probably.

thanks,
--a.

what does this "OR" mean : two cases , a switch in the definition of y(3)'
or what? the sign-case might be harmful if you have a bad initial guess
and a sign change occurs, such that a jump occurs in the course of integration
this will led to failure. also, if there exists several (isolated) solutions
then somewhere the jacobian of the system must become singular, and again with
a bad choice you will get trouble. did you try "shooting" to get an initial guess?
maybe if you begin with a low precision requirement first and then increase this
step by step, using interpolation of the old solution to get the new guess?
hth
peter
.

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