ODE45, ODE113 How to get the step size in advance?

Hi guys,

Is there any way to get the step size in advance from ODE45, ODE113?

Answer 1

[Jan]

No. These solver use adpative methods to determine the stepsize dynamically. Therefore you cannot get it without running the intergration.

Why do you need this?

[Antillar]

This is my dilemma:

I set my integration interval to say z=[0 5]. My initial conditions vary in discrete steps as a function of this length, i.e z0=[sech(z) tanh(z)].

[Jan]

I do not get the problem. You can define the interval and the initial conditions, because both do *not* depend on the stepsize.

Answer 2

[Friedrich]

Hi,

ODE45 and ODE113 have variable step size and this size is choosen during solving. So there is no stepsize you can get.

[Antillar]

Thank you. Is there some way I can "tap" into the decision made by ODE?

[Jan]

Of course you can modify the stepsize control in a copy (!) of ode45.m. But this is really unsual and I cannot imagine a good reason to do this. Therefore I still assume, that you need something else.

Answer 3

[Floris]

You can, if you so wish, set a maximum step size using odeset.

See: http://www.mathworks.se/help/techdoc/ref/odeset.html#f92-1039598

But this not really what you want, is it?

[Grzegorz Knor]

By the way, I wonder if you can determine the minimum step?

[Nader]

This is my query as well. Really vital to my programme. The equations are really nonlinear and it takes ages to complete one simulation. If I could control the minimum time step size, this would solve my problem. I have checked this in another commercial software, and I am 100% sure this solves the simulation time problem. Is there a way to control minimum step size in Matlab ODE functions?

[Torsten]

Try a stiff solver, e.g. ODE15S.

Best wishes

Torsten.

[Jan]

@Nader: The step size is not reduced arbitrarily in the solver, but such, that the error bounds are not exceeded. If you set a minimal step size and the integrator cannot satisfy the local discretization error, it stops with an error message - and it should do so. Fording the integrator to use too large steps leads to inaccurate results. Therefore I disagree, that this "solves" the problem. In opposite: If this works with another tool, it hides the fact, that the problem is not solved, but that you obtain a rough and perhaps completely wrong result.

Maybe your ODE is stiff. Then follow Torsten's suggestion.

ODE integrators and local optimization tools are fragile. You can get a "final value" even if you drive the tools apart from their specifications. Calling this a "result" without an analysis of the sensitivity (measure how the trajectory reacts to small variations of the inputs or parameters) is not scientifically correct. You can find many publications with such mistakes.