Second-order problems in time. Wave equation
Finite-difference method for evolution PDEs

In this section, we take a brief look at the numerical solution of a second-order hyperbolic linear partial differential equation. Although the problem addressed here presents certain difficulties, the numerical solution techniques are analogous to those we discussed in the previous sections, albeit with certain adaptations; in particular, the notions of order, consistency, stability and convergence are identical to those introduced in the context of parabolic problems. In this section, therefore, we shall confine ourselves to presenting the main results required to solve the wave equation numerically.