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A Stochastic Collocation Method for Delay Differential Equations with Random Input

Published online by Cambridge University Press:  03 June 2015

Tao Zhou
Tao Zhou*
Affiliation:
Institute of Computational Mathematics, Academy of Mathematics and Systems Sciences, The Chinese Academy of Sciences, Beijing 100190, China
*
*Corresponding author. Email: tzhou@lsec.cc.ac.cn
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Abstract

In this work, we concern with the numerical approach for delay differential equations with random coefficients. We first show that the exact solution of the problem considered admits good regularity in the random space, provided that the given data satisfy some reasonable assumptions. A stochastic collocation method is proposed to approximate the solution in the random space, and we use the Legendre spectral collocation method to solve the resulting deterministic delay differential equations. Convergence property of the proposed method is analyzed. It is shown that the numerical method yields the familiar exponential order of convergence in both the random space and the time space. Numerical examples are given to illustrate the theoretical results.

Keywords

65C2065M70Delay differential equationsstochastic collocationsparse gridlegendre spectral method
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 4 , August 2014 , pp. 403 - 418
Copyright
Copyright © Global-Science Press 2014

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