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Explicit vs. implicit FDM: Could you please suggest a reference?

The context is the finite difference modeling (FDM) of the transient diffusion equation (the linear one: $\dfrac{\partial T}{\partial t} = \alpha \dfrac{\partial^2 T}{\partial x^2}$).

Two approaches are available for modeling the evolution of $T$ in time: (i) explicit and (ii) implicit (e.g., the Crank-Nicolson method).

It was obvious to me that the explicit approach has a local (or compact) support whereas the implicit approach has a global support.

shuvo's picture


Computational field of solid mechanics is mostly dominated by FEM.   This is a well known topic.

But is it that  FDM (finite difference method) has no chance of surviving
in solid mechanics?

What are the present developments in the use of FDM in case of elasticity analysis of solid body?

I would like to mention some of the recent research works on this topic here.....

Recently a new mathematical model has been developed by Prof. S. Reaz Ahmed and his students known as the "displacement potential approach".

FEM Is Not a Local Method (and It Isn't Global Either)

In the literature, FEM has sometimes been characterized as a local approach, but IMO this needs to be corrected.

The piecewise continuous trial-functions of FEM can be looked at from two different viewpoints:

Why not use FDM in solid mechanics?

Finite Difference Method (FDM) and the related techniques such as FVM, are often found put to great use in fluid mechanics. See any simulation showing not only streamlines but also vortex shedding, turbulent mixing, etc.

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