Stability concepts and their applications

Imre Fekete, István Faragó

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The stability is one of the most basic requirement for the numerical model, which is mostly elaborated for the linear problems. In this paper we analyze the stability notions for the nonlinear problems. We show that, in case of consistency, both the N-stability and K-stability notions guarantee the convergence. Moreover, by using the N-stability we prove the convergence of the centralized Crank-Nicolson-method for the periodic initial-value transport equation. The K-stability is applied for the investigation of the forward Euler method and the θ-method for the Cauchy problem with Lipschitzian right side.

Original languageEnglish
Pages (from-to)2158-2170
Number of pages13
JournalComputers and Mathematics with Applications
Volume67
Issue number12
DOIs
Publication statusPublished - Jul 2014

Keywords

  • Convergence
  • Nonlinear stability
  • Transport problem

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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