DOI: https://doi.org/10.26089/NumMet.v21r107

An efficient software implementation of numerical methods for solving stiff systems of delay differential equations

Authors

  • D.A. Zheltkov
  • R.M. Tretiakova
  • V.V. Zheltkova
  • G.A. Bocharov

Keywords:

numerical methods
delay differential equations
stiff systems
linear multistep methods

Abstract

The systems of delay differential equation are widely used in modern mathematical modeling. The process of mathematical model development and identification requires the repeated solution of initial value problems for such systems. The numerical solution of delay differential equations may be computationally expensive, especially when the problem is stiff and high-dimensional. Therefore, it is important to develop and implement the efficient algorithms for the numerical solution of different classes of delay differential equations. In this paper, a new implementation of DIFSUBDEL program package for the numerical solution of delay differential equations based on linear multistep methods is discussed. The modified version is based on structured programming principles to make the program thread safe and user-friendly. The modified program performance is compared with the existing implementations of numerical methods for the solution of delay differential equations.

New computational technologies

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Published

2020-02-18

Issue

Vol. 21 (2020): Issue 1.

Section

Section 1. Numerical methods and applications

Author Biographies

D.A. Zheltkov

Marchuk Institute of Numerical Mathematics of RAS (INM RAS)
• Junior Researcher

R.M. Tretiakova

Marchuk Institute of Numerical Mathematics of RAS (INM RAS)
• Junior Researcher

V.V. Zheltkova

Marchuk Institute of Numerical Mathematics of RAS (INM RAS)
• Junior Researcher

G.A. Bocharov

Marchuk Institute of Numerical Mathematics of RAS (INM RAS)
• Leading Researcher

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