Time Discretization: Some Basic Approaches

Abstract

The basic concepts of stability, consistency and convergence are introduced. Additional measures of stability, such as A- and L-stability are discussed, along with desirable stability properties for the time integration of partial differential equations. The family of Runge–Kutta methods is reviewed, including both classical schemes and more recently developed strong-stability preserving and diagonally implicit methods. The chapter concludes with a brief discussion of linear multistep methods.