On collocation methods for delay differential and Volterra integral equations with proportional delay

doi:10.1007/s11464-009-0004-x

Front Math Chin

2009, Vol. 4

Issue (1) : 89-111 https://doi.org/10.1007/s11464-009-0004-x

RESEARCH ARTICLE

On collocation methods for delay differential and Volterra integral equations with proportional delay

Emiko ISHIWATA¹(

), Yoshiaki MUROYA²

1. Department of Mathematical Information Science, Tokyo University of Science, Tokyo 162-8601, Japan; 2. Department of Mathematics, Waseda University, Tokyo 169-8555, Japan

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Abstract

To compute long term integrations for the pantograph differential equation with proportional delay qt, 0 < q ≤ 1: y＇(t) = ay(t) + by(qt) + f(t), y(0) = y₀, we offer two kinds of numerical methods using special mesh distributions, that is, a rational approximant with ‘quasi-uniform meshes’ (see E. Ishiwata and Y. Muroya [Appl. Math. Comput., 2007, 187: 741-747]) and a Gauss collocation method with ‘quasi-constrained meshes’. If we apply these meshes to rational approximant and Gauss collocation method, respectively, then we obtain useful numerical methods of order p^? = 2m for computing long term integrations. Numerical investigations for these methods are also presented.

Keywords Delay differential equation proportional delay collocation quasiuniform mesh quasi-constrained mesh

Corresponding Author(s): ISHIWATA Emiko,Email:ishiwata@rs.kagu.tus.ac.jp

Issue Date: 05 March 2009

Cite this article:

Emiko ISHIWATA,Yoshiaki MUROYA. On collocation methods for delay differential and Volterra integral equations with proportional delay[J]. Front Math Chin, 2009, 4(1): 89-111.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-009-0004-x
https://academic.hep.com.cn/fmc/EN/Y2009/V4/I1/89

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