[AlexeyBrin]

You mean the concept of a sparse matrix ? Well, for e.g. if you use FEM (Finite Element method) you usually end up with a huge linear system which has the nice property that more than 90% of his coefficients are zeros. A sparse matrix will store only the non-zero elements, this is a huge gain from the point of view of memory usage.

Similar considerations applies for using Finite Difference methods.

[turbojerry]

They are also at the heart of the SPICE circuit simulator[1]

[1] http://en.wikipedia.org/wiki/SPICE#Introduction

[frozenport]

Although for finite difference schemes we dont usually form the matrix but rather perform convolution/ forward stencil math.