Fractional-Step Block Method For Direct Solution Of Third Order Ordinary Differential Equations (IVPS)
DOI:
https://doi.org/10.59846/ajbas.v3i1.594Keywords:
power series, grid points, convergence, interpolation, collocationAbstract
This article produced a one-eight linear multi-step method for the numerical integration of third-order initial value problems (IVPs) of ordinary differential equations (ODEs). The method was achieved by considering the power series polynomial as an approximate solution using the techniques of interpolation and collocation. The resulting equations were solved for the unknown parameters and substituted into the approximate solution to the problem to obtain the required discrete and additional formulas that constituted the proposed block method. Analysis of the basic properties of the method reveals that it has theoretical order five, zero stable, consistent, convergence, and absolute stability. The numerical experiment results showed that the method compares well with the three cited methods in literature and has the potential to solve non-linear third-order ODEs.
References
Francis, M. M.,Benard, O.B., Richard, M. and Omolo O. (2023) Mathematical Analysis of COVID-19 model with Vaccina-tion and Partial Immunity to Reinfection. Journal of Mathe-matical Analysis and Modeling.. 4(2): 121-145 doi:10.48185/jmam.v4i2.942
Eiman, K. S., Muhammad, S. and Thabet A. (2024): On rota-virus infections disease model using piecewise modified ABC fractional order derivatives. AIMS Press. NHM, 19(1): 214–234. DOI: 10.3934/nhm.2024010
Muhammad R., Kamal S., Thabet A.,, Inas A., Asma Al Jaser4 and Manar A.(2024): A comprehensive analysis of COVID 19 nonlinear mathematical model by incorporating the environment and social distancing. Scientific Reports. (2024) 14:12238 |https://doi.org/10.1038/s41598-024-61730-y
Aziz K., Kamal S., Thabet A. and Inas A.(2024): Fractal frac-tional model for tuberculosis: existence and numerical solu-tions. Scientific Reports. (2024) 14:12211 https://doi.org/10.1038/s41598-024-62386-4
Lambert, J.D. (1973). Computational Methods in Ordinary Differential Equations.John Wiley, New York
Fatunla, S.O.,(1988). Numerical Methods for Initial value Problems in Ordinary Differential Equations. Academic Press Inc., New York
Bun, R.A., and Vasil’Yer, Y.D., (1992). A Numerical Method for Solving Differential Equations of any orders. Comp. Math. phys, 32, Pp 317-330
Awoyemi, D. O (1999): A class of continuous Methods for general second order initial value problems in ordinary dif-ferential equations. International journal of computer mathematics 72; 29-39.
Ademiluyi R.A., Duromola M.K. and Bolarinwa Bolaji (2014) Modified Block Method for the Direct Solution of Initial Value Problems of Fourth Order Ordinary Differen-tial Equations. Australian Journal of Basic and Applied Sciences, 8(10) July 2014, Pages 389-394
Kayode S.J, Duromola M. K and Bolarinwa Bolaji (2014): Direct solution of initial value problems of fourth order or-dinary differential equations using modified implicit hybrid block method. Journal of Scientific Research and Reports. 3(21); 2792 -2800
Duromola M.K. and Bolarinwa Bolaji (2016). Fractional Step Method for the Numerical Integration of Initial Value Problems of Third Order Ordinary Differential Equations. Journal of Nigerian Association of Mathematical Physics, Vol. 36,(July, 2016), Pp 23-30
Duromola M.K. (2022) Single-Step Block Method of P-Stable for Solving Third Order Differential Equations (IVPs): Ninth Order of Accuracy. American Journal of Ap-plied Mathematics and Statistics, 2022, Vol. 10, No. 1. Pp 4-13
Duromola M. K., Kayode S. J., and Lawal R. S. (2023). Linear Hybrid Multistep Block Method for Direct Solution of Initial Value Problems of Third Order Ordinary Differ-ential Equations. Asian Research Journal of Mathematics 19(11), Pp 175-190
M.K. Duromola. R.S. Lawal and O.M. Akinmoladun (2024): Numerical integration of linear hybrid multistep block method for third-order ordinary differential equations (IVPs). Scientific Africa https://doi.org/10.1016/j.sciaf.2024.e02129
Duromola, M.K and Momoh A.L.,(2019). Hybrid numerical method with block extension for direct solution of third order ordinary differential equation. Pacific Journal of Science and Technology.10(2),248254.
D.O. Awoyemi, E. A. Adebile, A.O. Adesanya and T.A. Anake (2011). Modified block method for the direct so-lution of second order ordinary differential equations. In-ternational Journal of Applied Mathematics and Compu-tation Volume 3(3),pp 181–188
Y. A. Yahaya and A. M. Badmus (2009). A class of collo-cation for General Second Order Ordinary Differential Equations. African Journal of Mathematics and Comput-er Science Research,2(4):069-072
Fatunla, S. O (1991). Block method for Second Order IVPs. International Journal of Computer Mathematics, 41(9); 55-63
Henrici P. (1962). Discrete Variable Method in Ordinary Differential Equations. John Wiley and Sons, New York
Anake, T. A., Adesanya, A.O, Oghonyon, G.J and Agarana, M.C. (2013). Block Algorithm for General Third Order Ordinary Differential Equations, ICASTOR Journal of Mathematical Sciences, 7(2), 127 -136
Adoghe Lawrence Osa and Omole Ezekiel Olaoluwa (2019). A Fifth-fourth Continuous Block Implicit Hybrid Method for the Solution of Third Order Initial Value Problems in Ordinary Differential Equations. Applied and Computa-tional Mathematics DOI: 10.11648/j.acm.20190803.11
Obarhua, F.O. and Kayode, S.J. (2016) Symmetric Hybrid Linear Multistep Method for General Third Order Differ-ential Equations. Open Access Library Journal, 3: e2583. http://dx.doi.org/10.4236/oalib.1102583
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Monday Kolawole Duromola, Olusegun Akinmoladun , Damilola Kolawole
This work is licensed under a Creative Commons Attribution 4.0 International License.
