Chapter 17 - TIME DEPENDENT PROBLEMS

Abstract

This chapter provides an overview of time dependent problems. Many problems require the solution of time-dependent equations. In this context, there are numerous theoretical topics that an analyst should investigate before selecting a computational algorithm. These include the stability limits, amplitude error, and phase error. A large number of implicit and explicit procedures have been proposed. The chapter mentions typical additional computational procedures that arise in the time integration problems. It illustrates both simple explicit and implicit algorithms. Applications involving second-order spatial derivatives and first-order time derivatives will be referred to as parabolic or transient, while those with second-order time derivatives will be referred to as hyperbolic or dynamic. For these classes of problems, it is common to select various temporal operators to approximate the time derivatives. The actual time integration algorithm is determined by the choices of the difference operators and the ways that they are combined.