A New Multi-Step Method for Solving Delay Differential Equations using Lagrange Interpolation

Authors

  • V. J. Shaalini Department of Mathematics, Bishop Heber College, Trichy, India
  • S. E. Fadugba Department of Mathematics, Ekiti State University, Ado Ekiti, Nigeria

Keywords:

Multi-step method, delay differential equations, interpolating function, Lagrange interpolation, stability polynomial and stability region.

Abstract

This paper presents 2-step p-th order (p = 2,3,4) multi-step methods that are based on the combination of both polynomial and exponential functions for the solution of Delay Differential Equations (DDEs). Furthermore, the delay argument is approximated using the Lagrange interpolation. The local truncation errors and stability polynomials for each order are derived. The Local Grid Search Algorithm (LGSA) is used to determine the stability regions of the method. Moreover, applicability and suitability of the method have been demonstrated by some numerical examples of DDEs with constant delay, time dependent and state dependent delays. The numerical results are compared with the theoretical solution as well as the existing Rational Multi-step Method2 (RMM2). 

Dimensions

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Published

2021-08-29

How to Cite

A New Multi-Step Method for Solving Delay Differential Equations using Lagrange Interpolation. (2021). Journal of the Nigerian Society of Physical Sciences, 3(3), 159-164. https://doi.org/10.46481/jnsps.2021.247

Issue

Volume 3, Issue 3, August 2021

Section

Original Research
Copyright & Licensing

Copyright (c) 2021 Journal of the Nigerian Society of Physical Sciences

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

A New Multi-Step Method for Solving Delay Differential Equations using Lagrange Interpolation. (2021). Journal of the Nigerian Society of Physical Sciences, 3(3), 159-164. https://doi.org/10.46481/jnsps.2021.247