Time integration methods

Abstract

The process of semi-discretization discussed in chapter 6 produces a system of ordinary differential equations with respect to time:

$$M\frac{d\textup{v}}{dt}+A\;\textup{v}=0$$

((8.1))

where v contains all unknowns and M is a “mass matrix”; it is nontrivial in finite-element methods but is unity in most other cases. The number of equations equals the number of grid-point values and may be very large. Several standard numerical methods exist to integrate such systems of differential equations. They are reviewed in sections 8.2–8.3.