# Shooting method for non-oscillatory solutions

I am having some trouble with using the shooting method : I am given a system of ode's representing initial value problem, and I know I want one of the unknowns (=u) to vanish at infinity (which I took for simplicity to be 30).

The problem is that when I am using the shooting method (I have a one-dimensional shooting. i.e.- only one of the unknowns is undetermined in (0) ), I get an oscillatory solution (the oscillations have a growing amplitude) that indeed satisfy u(30)=0, but it doesn't approach 0 uniformly (rather, it is $10^{23}$ right before 30) . The ODE becomes unstable in the direction I am shooting, so that the dominant mode completely contaminates the search for the subdominant boundary condition

Is there any suitable method for such a case ? (i.e.- I am looking for a variant of the shooting method that is able to look for a solution at infinity which is not oscillatory. rather, it should approach 0 a smooth way)

Hope I made myself clear enough.

• @IgorKhavkine : thanks a lot for your suggestion for a more appropriate forum and for your answer. I edit my first post , and included your explanation in it. Hope it is ok. Indeed, the problem is that the ODE is unstable in the vicinity of 30, and the oscillations amplitude becomes very large (it is expected to be bounded, but increases to $10^23$ and more) . I have tried shooting in the other direction, but still, I prefer to use the shooting in this direction (I know the values of all of the relevant derivaties in 0, which I do not know in 30) – NumericsWannabe Jan 2 '15 at 7:10