Journal of Applied Mathematics

Convergence and Stability in Collocation Methods of Equation u ( t ) = a u ( t ) + b u ( [ t ] )

Han Yan, Shufang Ma, Yanbin Liu, and Hongquan Sun

Full-text: Open access

Abstract

This paper is concerned with the convergence, global superconvergence, local superconvergence, and stability of collocation methods for u ( t ) = a u ( t ) + b u ( [ t ] ) . The optimal convergence order and superconvergence order are obtained, and the stability regions for the collocation methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained, and some numerical experiments are given.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 125926, 17 pages.

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357153580

Digital Object Identifier
doi:10.1155/2012/125926

Mathematical Reviews number (MathSciNet)
MR2997258

Zentralblatt MATH identifier
1264.65127

Citation

Yan, Han; Ma, Shufang; Liu, Yanbin; Sun, Hongquan. Convergence and Stability in Collocation Methods of Equation ${u}^{\prime }(t)=au(t)+bu([t])$. J. Appl. Math. 2012 (2012), Article ID 125926, 17 pages. doi:10.1155/2012/125926. https://projecteuclid.org/euclid.jam/1357153580


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