Numerical Analysis and Applicable Mathematics
Title
The Approximate Solution of First Order Delay Differential Equations Using Extended Third Derivative Block Backward Differentiation Formulae
Authors
Chibuisi C.,a Uchendu K.b and Osu B.O.*b,c
aDepartment of Insurance, University of Jos, Jos, Nigeria.
bDepartment of Statistics, Michael Okpara University of Agriculture, Umudike, Nigeria.
cDepartment of Mathematics, Abia State University, Uturu, Nigeria.
*Corresponding author E-mail address: osu.bright@mouau.edu.ng (B.O. Osu)
Article History
Publication details: Received: 01st February 2021; Revised: 11th June 2022; Accepted: 13th June 2022; Published: 18th June 2022
Cite this article
Chibuisi C.; Uchendu K.; Osu B.O. The Approximate Solution of First Order Delay Differential Equations Using Extended Third Derivative Block Backward Differentiation Formulae. Numer. Anal. Appl. Math., 2022, 3(5), 1-10.
Abstract
The formulation of extended third derivative block backward differentiation formulae was presented for the solution of first order delay differential equations (DDEs) without the application of interpolation techniques in computing the delay term. The delay term was computed by a valid expression of sequence. By matrix transposition procedure, the discrete schemes of the proposed method were carried-out through its continuous derivations with the help of linear multistep collocation approach. The convergence and stability analysis of the method were satisfied. The performances of the proposed method on numerical experiments of some first order DDEs revealed that the scheme for step number k = 4 performed better and faster in terms of efficiency, accuracy, consistency, convergence, region of absolute stability and Central Processing Unit Time (CPUT) at fixed step size than the schemes for step numbers k = 3 and 2 when compared with their exact solutions and other existing methods.
Keywords
First order delay differential equations; extended third derivative backward differentiation formulae; block method
