Stiff differential equation solvers

I'm trying to understand how the stiff differential equations are solved in ode5s and ode15i.

If my understanding is right, stiff equation solver implements BDF method if specified in the option given in the call to the solver.

What happens in implicit solver?

e.g. if dx/dt = f(x,t)

is written as

x(n+1) = x(n) + f(x(n),tn) + f(x(n+1),t(n+1))

Is it solved using non-linear equation solver?

Could someone explain? Is there any example files that are available for implementation of BDF and implicit solver?

[Torsten]

You shouldn't try to program your own implicit solver.

If the MATLAB solvers are not capable to handle your equations, it is very optimistic to think that your own handmade code will succeed.

[Deepa Maheshvare]

Yes, I understand. It would be challenging to write efficient algorithms that are implemented in MATLAB.

I got a little confused while reading about different solvers. My equations are stiff, therefore I am looking for a stiff equation solver.When I tried ode15i , it didn't work. ode15s works for me.

In the documentation it is mentioned that ode15s used BDF. From what I understand, BDF is implicit method. I'm trying to get clarification on whether ode15s is also an implicit solver.

[Torsten]

All stiff solvers are implicit.

But I can't understand how you solved your problem using ode15s because your equations contain products of time derivatives.

[Deepa Maheshvare]

Thank you.I had an understanding that ode15s wasn't implicit. Now, it is clear to me that it is an implicit solver.

I'm sorry if any of the notations that I used wasn't clear. My equations are ode's which come from convection-reaction-diffusion system. The functions on the RHS contain variables that are functions of time, but not time derivatives.

[Torsten]

Forget my comment.

I mixed your problem up with another one.

[Deepa Maheshvare]

No issues

Answer 1

[Steven Lord]

There are several stiff solvers. See the "Basic Solver Selection" section on this documentation page for a table indicating which solvers are stiff and which are nonstiff. For more details about a particular solver, see the Algorithms and References sections on each solver's documentation page.