Time-dependent equations

  • Roger Peyret
Part of the Applied Mathematical Sciences book series (AMS, volume 148)

Abstract

In this chapter, we discuss the time-discretization of time-dependent equations. Although the methods apply to general nonlinear time-dependent equations, their analysis is developed in the linear case and, more especially, for the advection-diffusion equation. First, we address the stability of the spectral approximation, namely, the existence of a bounded solution of the differential equations in time resulting from the spectral approximation. Then the major part of the chapter is devoted to the presentation and discussion of the accuracy and stability of the time-discretization schemes. Second- and higher-order methods are considered in the following two cases: two-step methods (essentially based on Backward-Differentiation and Adams-Bashforth schemes) and one-step methods (Runge-Kutta schemes). The chapter ends with a comparison between the different kinds of time-discretization schemes.

Keywords

Explicit Scheme Chebyshev Approximation Chebyshev Collocation Method Fourier Approximation Multistep Scheme 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Roger Peyret
    • 1
  1. 1.Laboratoire J.A. DieudonnéUniversité de Nice-Sophia AntipolisNiceFrance

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