Collocation methods for differential equations with piecewise linear delays

Hui Liang; Hermann  Brunner

doi:10.3934/cpaa.2012.11.1839

Article Contents

2012, Volume 11, Issue 5: 1839-1857. Doi: 10.3934/cpaa.2012.11.1839

This issue Previous Article Existence and uniqueness of positive solution to a non-local differential equation with homogeneous Dirichlet boundary condition---A non-monotone case Next Article On a singular Hamiltonian elliptic systems involving critical growth in dimension two

Collocation methods for differential equations with piecewise linear delays

Hui Liang^1, and
Hermann Brunner^2,

1.
School of Mathematical Sciences, Heilongjiang University, Harbin, Heilongjiang
2.
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR

Received: March 2011

Revised: September 2011

Published: September 2012

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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.

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Mathematics Subject Classification: 65L03, 34K06, 34K28.

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