An Examination of the Accuracy and Zero Stability of the Explicit Linear Two-Step Method for Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs)

S.E. Fadugba¹

Section:Research Paper, Product Type: Journal-Paper
Vol.7 , Issue.3 , pp.28-32, Jun-2020

Online published on Jun 30, 2020

Copyright © S.E. Fadugba . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper, an explicit linear two-step method of maximal order containing one free parameter for the solution of IVPs in ODEs is presented. The performance measure of the method in terms of the accuracy and zero stability is examined. The bound of the local truncation error for the explicit linear one-step method has been investigated. Numerical example has been solved successfully via the explicit linear two-step method by varying the free parameter. The results obtained show that the explicit linear two-step method is zero stable and agrees with the exact solution. In the case of b = -5, the method is zero unstable. It can also be concluded that one order decrease in the values of the step length leads to third order decrease in the magnitude of the error bound of the method. The methodology can be applied to the solution of higher order ODEs emanated from real life situations with points of catastrophe.

Key-Words / Index Term :
Bound, Explicit linear two-step method, Initial value problem, Local truncation error, Exact solution

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