Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Collocation methods for differential equations with piecewise linear delays

Language

English

Abstract

After analyzing the regularity of solutions to delay differential equations (DDEs) with piecewise continuous (linear) non-vanishing delays, we describe collocation schemes using continuous piecewise polynomials for their numerical solution. We show that for carefully designed meshes these collocation solutions exhibit optimal orders of global and local superconvergence analogous to the ones for DDEs with constant delays. Numerical experiments illustrate the theoretical superconvergence results.

Keywords

Collocation methods, Delay differential equations, Optimal order of superconvergence, Piecewise non-vanishing delays, Regularity of solutions

Publication Date

2012

Source Publication Title

Communications on pure and applied analysis

Volume

11

Issue

5

Start Page

1839

End Page

1857

Publisher

American Institute of Mathematic

DOI

10.3934/cpaa.2012.11.1839

Link to Publisher's Edition

http://dx.doi.org/10.3934/cpaa.2012.11.1839

ISSN (print)

15340392

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