Explicit time discretization

Abstract

In this chapter, we consider the same space semi-discrete problem as in the previous chapter, but we now discretize it in time using an explicit scheme. We first discuss generic properties of explicit Runge–Kutta schemes (ERK). Then we analyze the explicit Euler scheme, second-order two-stage ERK schemes, and third-order three-stage ERK schemes. The key advantage of explicit schemes over implicit schemes is that the linear algebra at each time step is greatly simplified since one has to invert only the mass matrix. However, the stability of ERK schemes requires that the time step be limited by a CFL-like condition.