Posted by Lautaro Vergara on December 16, 1997 at 09:53:25:

Could somebody give some hints about how could I solve

the following stiff ODE?:

(x*y'(x)-3*y(x)=-1/sqrt(2+2*y'+4*x*y'') (1)

with BCs

3*y(0)=1/sqrt(2+2*y'(0))

(2)

y(X)=A*X**3+1/(4*sqrt(30*A)*X)

where X is a suitably chosen 'asymptotic' value

(that could well be 1 or 2) and A is a parameter

that must be numerically found, such that the solution

does not diverge within the interval [0,X].

This is just an example for a more involved set of

coupled nonlinear ODEs of the form

F(y',y,x)=int(G(y'',y',y,x,P),P=1..infinity)

where F is a simple function of their arguments,

like the LHS in (1), the integrals are all finite

(as in the RHS of (1)), G is more complicated but

well behaved function. The BCs that involve a set of

unknown parameters, like A above, that must be

found such that the solutions are finite. The BCs

are such that it there exists at most a discrete

set of acceptable solutions (this is known).

I have tried to implement relaxation, as in

Numerical Recipes, but I have found serious

problems.

I have also converted eq. (1) above as a DAE, but

I have found no code that could sove such system,

when the BCs are NOT consistent (COLDAE does this,

but only for consistent BCs).

I shall appreciate very much some hints about

this or information about a program that could

serve as a basis for solving such kind of problems.

Thank you very much in advance.

Sincerely,

Lautaro Vergara