Finite Difference Methods

In Collatz’s famous 1950 monograph Numerical Treatment of Differential Equations, the following statement can be found: The finite difference method is a procedure generally applicable to boundary value problems. It is easily set up and on a coarse mesh it generally supplies, after a relatively short calculation, an overview of the solution function that is often sufficient in practice. In particular there are classes of partial differential equations where the finite difference method is the only practical method, and where other procedures are able to handle the boundary conditions only with difficulty or not at all.