Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10346133 | Computers & Mathematics with Applications | 2014 | 13 Pages |
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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Imre Fekete, István Faragó,