Numerical Analysis and Applicable Mathematics
Title
Numerical Solution of Stochastic Delay Differential Equations Using Block Backward Differentiation Formulae Methods
Authors
Numerical Solution of Stochastic Delay Differential Equations Using Block Backward Differentiation Formulae Methods
B. O. Osu*a and C. Chibuisib
aDepartment of Mathematics, Abia State University Uturu, Nigeria.
bDepartment of Insurance, University of Jos, Jos, Nigeria.
*Corresponding author E-mail address: osu.bright@mouau.edu.ng (B. O. Osu)
Article History
Publication details: Received: 19th June 2022; Revised: 03rd December 2022; Accepted: 03rd December 2022; Published: 20th December 2022
Cite this article
Osu B. O.; Chibuisi C. Numerical Solution of Stochastic Delay Differential Equations Using Block Backward Differentiation Formulae Methods. Numer. Anal. Appl. Math., 2022, 3(6), 39-50.
Abstract
This paper presents the application of Block Backward Differentiation Formulae Methods for the numerical solution of Stochastic Delay Differential Equations with two new formulated expressions for evaluation of the delay terms. This was carried-out by formulating a continuous representation of the proposed method through multistep collocation method by matrix inversion technique. After the evaluation and simplification of the continuous representations of each step number, the discrete schemes were obtained. The convergence and stability analysis of the method were investigated. The performances of the method were demonstrated by solving some stochastic delay differential equations to show the accuracy and efficiency advantages over other existing methods. It was observed that the scheme for step number k = 4 performed slightly better and faster in terms of accuracy than the schemes for step number k = 2 and 3 respectively when compared with the exact solutions.
Keywords
Stochastic delay differential equations; block method; linear multistep method
