Open AccessA New Multi-Step Method for Solving Delay Differential Equations using Lagrange Interpolation
Author(s) -
V. J. Shaalini,
Sunday Emmanuel Fadugba
Publication year - 2021
Publication title -
journal of the nigerian society of physical sciences
Language(s) - English
Resource type - Journals
ISSN - 2714-4704
DOI - 10.46481/jnsps.2021.247
Subject(s) - lagrange polynomial , delay differential equation , mathematics , interpolation (computer graphics) , truncation error , stability (learning theory) , truncation (statistics) , polynomial , polynomial interpolation , numerical stability , differential equation , numerical analysis , mathematical analysis , linear interpolation , computer science , animation , statistics , computer graphics (images) , machine learning
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).