How is solving a piecewise linear ode going to be different than solving a regular linear ode?

Question

anonymous · Answer

It just means that each piece is linear within it's domain, allowing an analytic solution (ie the function is not smooth globally).

Course, you or the computer have to do the solving for as many pieces as there are.

anonymous · Answer

So I'm going to end up with two answer?

anonymous · Answer

Well, you're going to end up with data computed according to the definition for a piece ie if input1 is in piece1, you calculate output according to the function definition for piece 1.

To say you end up with 2 answers is an oversimplification, you have a system of ODE's if you like, that you can analyze more or less qualitatively in support of  some numerical method (piecewise definitions don't sit well in simulations because of the stepping effect, if you graphed the function it would have discontinuities or sudden changes in direction.).

Also there are different kinds of piecewise systems.

anonymous · Answer

I'll just put up the problem.  Let me know what you think.