What method does pdepe use to solve PDE's

Can anyone advise what numerical technique the pdepe is using to solve my PDE's?

Answer 1

[Torsten]

See the reference for pdepe:

Skeel, R. D. and M. Berzins, "A Method for the Spatial Discretization of Parabolic Equations in One Space Variable," SIAM Journal on Scientific and Statistical Computing, Vol. 11, 1990, pp.1–32.

It's an implementation of the method-of-lines together with a finite-element discretization in space.

Best wishes

Torsten.

[Kevin Lambert]

Thanks Torsten Having read that paper briefly and the mathworks guide to FEM, would it be fair to say that the method of lines is used in instances where m=0 and FEM when m>0

[Torsten]

No.

The spatial derivatives are discretized and the time derivatives are held continuous - that's the (vertical) method-of-lines. The way how the spatial derivatives are discretized is according to FEM.

Best wishes

Torsten.

[Alessandro Ferreri]

If I understand correctly, the spatial discretization is achieved by FEM and we are left with Differential algebraic equations with time derivatives. What method does ode15s employ to solve these equations?