Stability concepts and their applications

Imre Fekete; István Faragó

doi:10.1016/j.camwa.2014.02.024

Stability concepts and their applications

Imre Fekete^*
, István Faragó

^*Corresponding author for this work

Eötvös Loránd University

Research output: Contribution to journal › Article › peer-review

Abstract (may include machine translation)

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 language	English
Pages (from-to)	2158-2170
Number of pages	13
Journal	Computers and Mathematics with Applications
Volume	67
Issue number	12
DOIs	https://doi.org/10.1016/j.camwa.2014.02.024
State	Published - Jul 2014
Externally published	Yes

Keywords

Convergence
Nonlinear stability
Transport problem

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10.1016/j.camwa.2014.02.024

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AU - Faragó, István

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AB - 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.

KW - Convergence

KW - Nonlinear stability

KW - Transport problem

UR - https://www.scopus.com/pages/publications/84902536212

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JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 12

ER -

Stability concepts and their applications

Abstract (may include machine translation)

Keywords

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