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Constraints on guesses for Shooting Method solution to boundary value problems
I have a 2x2 system of (highly) nonlinear-ODEs. I am pretty sure the system is not stiff. One variable, x(t), has an initial condition. The second variable, s(t), has a boundary value at infinity. A stable, stationary saddle-path equilibrium exists with a known value of s(\infinity). The variables will only be solved within a particular range i.e. for all t, 0 < x(t) < B_1, 0 < s(t) < B_2 for some constants B. At the boundaries of these ranges, the system of ODEs would be singular, but the solution to the ODE wouldn't have any problems with divergence for any x(0) in the valid range. I am choosing a large terminal value for time and trying to solve some dynamics of the system using NDSolve. I have tried using Method -> Shooting and setting the StartingInitialConditions. Regardless of what I try, Mathematica is telling me that the system is likely singular or stiff. My guess is: In its calculation of shooting guesses, it is choosing some s(0) which is at the singularity (e.g. it chooses s(0)=0 or s(0) > B). So my question is: how can I give constraints to Mathematica to tell it not to guess initial conditions outside of the acceptable range?