MODELING STOCHASTIC ADVERSE EFFECTS OF CBN 2023 REDESIGNED NAIRA NOTES POLICY ON RURAL FARMERS IN NIGERIA
Abstract
The recent Central Bank of Nigeria (CBN) 2023 redesigned naira notes is of good benefits to strengthen the economy of the country by checking counterfeiting and hoarding of large volume of banknotes by the public. Despite all the efforts made by the CBN for citizens to enjoy the benefits of this implementation, most rural farmers were faced with adverse effects of uncertainties in the production and marketing of their agricultural produce due to lack of redesigned new naira notes in circulation. The adverse effects of these uncertainties are modeled as Advanced Stochastic Time-Delay Differential Equation (ASTDDE). The modeled equation is solved using Extended Second Derivative Block Backward Differentiation Formulae Method (ESDBBDFM) without the use of interpolation techniques in the evaluations of the delay term and noise term. In comparing the numerical results of this method with other existing methods in literature, the newly developed mathematical expressions for the evaluations of the delay term and the noise term in solving ASDDEs with the discrete schemes of ESDBBDFM gives better results for step number than step numbers and 3 by producing Least Minimum Absolute Random Error (LMARE) in a Lower Computational Processing Unit Time (LCPUT) faster than other existing methods that applied interpolation techniques in evaluations of the delay term and the noise term.
Downloads
References
B. Evelyn, “Introduction to the Numerical Analysis of Stochastic Delay Differential Equations,” ,”Journal of Computational and Applied Mathematics, vol. 125, no. 03, pp. 297–307, 2000.
O. O. Ugbebor, “MATH 352 Probability Distribution and Elementary Limit Theorems,” University of Ibadan, Ibadan, 1991.
C. Adurayemi and O. State, “Cashless policy and its effects on the Nigerian Economy,” Journal of Economics and Financial Studies, vol. 4, no. 2, pp. 81–88, 2016.
“Draft 2017 Annual report, Central Bank of Nigeria,” 2018. Accessed: Nov. 15, 2018. [Online]. Available: ://www.cbn.gov.ng/Out/2018/RSD/CBN%202017%20ANNUAL%20REPORT_WEB.pdf
B. Akhtari, E. Babolian, and A. Neuenkirch, “An Euler Scheme for Stochastic Delay Differential Equations on Unbounded Domains: Pathwise Convergence,” Discrete Contin.Dyn. Syst., Ser.B, vol. 20, no. 1, pp. 23–38, 2015.
H. M. Radzi, Z. A. Majid, and F. Ismail, “Solving Delay Differential Equations by the Five-point One-step Block Method Using Neville’s Interpolation,” International Journal of Computer Mathematics, vol. 90, no. 7, pp. 1459–1470, 2012, [Online]. Available: http://dx.doi.org/10.1080/00207160.754015
B. Akhtari, “Numerical solution of stochastic state-dependent delay differential equations: convergence and stability,” Adv Differ Equ, vol. 2019, no. 1, p. 396, Dec. 2019, doi: 10.1186/s13662-019-2323-x.
B. O. Osu, C. Chibuisi, C. Olunkwa, and C. F. Chikwe, “Evaluation of Delay Term and Noise Term for Approximate Solution of Stochastic Delay Differential Equation without Interpolation Techniques,” Global Journal of Engineering and Technology [GJET], vol. 2, no. 9, pp. 1–19, 2023.
P. Onumanyi, D. O. Awoyemi, S. N. Jator, and U. W. Sirisena, “New Linear Multistep Methods with Continuous Coefficients for First Order Initial Value Problems,” Journal of Nigerian Mathematical Society, vol. 13, no. 3, pp. 37–51, 1994.
J. D. Lambert, Computational Methods in Ordinary Differential Equations. New York, USA: John Willey and Sons Inc, 1973.
G. Dahlquist, “Convergence and Stability in the Numerical Integration of Ordinary Differential Equations,” Math, Scand., vol. 4, no. 5, pp. 33–53, 1956.
C. Chibuisi, B. O. Osu, C. Granados, and O. S. Basimanebotlhe, “A Class of Seventh Order Hybrid Extended Block Adams Moulton Methods for Numerical Solutions of First Order Delay Differential Equations,” Sebha University Journal of Pure & Applied Sciences, (JOPAS), vol. 21, no. 1, pp. 94–105, 2022.
C. Chibuisi, B. O. Osu, C. Olunkwa, S. A. Ihedioha, and S. Amaraihu, “Computational Treatment of First Order Delay Differential Equations Using Hybrid Extended Second Derivative Block Backward Differentiation Formulae,” European Journal of Mathematics and Statistics, vol. 1, no. 1, Dec. 2020, doi: 10.24018/ejmath.2020.1.1.8.
B. O. Osu, C. Chibuisi, G. A. Egbe, and & V. C. Egenkonye, “The Solution of Stochastic Time-Dependent First Order Delay Differential Equations Using Block Simpson’s Methods,” International Journal of Mathematics and Computer Applications Research (IJMCAR), vol. 11, no. 1, pp. 1–20, 2021.
U. W. Sirisena and S. Y. Yakubu, “Solving delay differential equation using reformulated backward differentiation methods,” Journal of Advances in Mathematics and Computer Science, vol. 32, no. 2, pp. 1–15, 2019.
Copyright (c) 2024 Bright Okore Osu, Chigozie Chibuisi, Edikan Edem Akpanibah
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this Journal agree to the following terms:
- Author retain copyright and grant the journal right of first publication with the work simultaneously licensed under a creative commons attribution license that allow others to share the work within an acknowledgement of the work’s authorship and initial publication of this journal.
- Authors are able to enter into separate, additional contractual arrangement for the non-exclusive distribution of the journal’s published version of the work (e.g. acknowledgement of its initial publication in this journal).
- Authors are permitted and encouraged to post their work online (e.g. in institutional repositories or on their websites) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published works.
1.gif)
