Simulating the Dynamics of Oscillating Differential Equations of Mass in Motion
DOI:
https://doi.org/10.62054/ijdm/0101.07Abstract
This research explores the practical implementation and simulation of oscillatory differential equations concerning objects in motion. The methodology incorporates power series polynomials, ensuring adherence to the fundamental properties of these functions. The novel approach is applied to various oscillatory differential equations, encompassing harmonic motion, spring motion, dynamic mass motion, Betiss and Stiefel equations, and nonlinear differential equations. The results demonstrate computational reliability, showcasing enhanced accuracy and quicker convergence compared to currently examined methods.
Dynamic motion, Genesio, Harmonic motion, Mass, Spring of motion
References
Blanka B. (2019). Oscillation of second-order nonlinear non-canonical differential equations with deviating
argument. Applied Mathematics Letters, 91, 68–75.
Kusano, T., Naito, Y. (1997). Oscillation and nonoscillation criteria for second order quasilinear differential
equations. Acta Math. Hungar, 76, 81–99.
Agarwal, R.P., Grace, S.R., O’Regan, D. (2003). Oscillation Theory for Second Order Dynamic Equations. Taylor
Francis.
Bainov, D.D., Mishev, D.P. (1991). Oscillation Theory for Neutral Differential Equations with Delay. Adam Hilger.
Agarwal, R.P., Bohner, M., Li, T., Zhang, C. (2013). A new approach in the study of oscillatory behavior of even-
order neutral delay differential equations. Appl. Math. Comput, 225, 787–794.
Triana, C.A., Fajardo, F. (2013). Experimental study of simple harmonic motion of a spring-mass system as a
function of spring diameter. Revista Brasileira de Ensino de Física, 35(4), 4305.
Saker, S. (2010). Oscillation Theory of Delay Differential and Difference Equations: Second and Third Orders.
LAP Lambert Academic Publishing.
Triana, C.A., Fajardo, F. (2013). Experimental study of simple harmonic motion of a spring-mass system as a
function of spring diameter. Revista Brasileira de Ensino de Física, 35(4), 4305.
French, A.P. (1964). Vibrations and Waves. Norton.
Donald, J. Z., Skwame, Y., Sabo, J., Ayinde, A. M. (2021). The use of linear multistep method on implicit one-step
second derivative block method for direct solution of higher order initial value problems. Abacus (Mathematics
Science Series), 48(2), 224-237.
Fatunla, S.O. (1980). Numerical integrators for stiff and highly oscillatory differential equations. Math Comput., 34,
-390.
Skwame, Y., Bakari, A. I., Sunday, J. (2017). Computational method for the determination of forced motions in
mass-spring systems. Asian Research Journal of Mathematics, 3(1), 1-12.
Sabo, J., Kyagya, T. Y., Vashawa, W. J. (2021). Numerical simulation of one step block method for treatment of
second order forced motions in mass spring systems. Asian Journal of Research and Reviews in Physics, 5(2),
-11.
Omole, E. A., Ogunware, B. G. (2018). 3-point single hybrid block method (3PSHBM) for direct solution of
general second order initial value problem of ordinary differential equations. Journal of Scientific Research
Reports, 20(3), 1-11.
Olanegan, O. O., Ogunware, B. G., Alakofa, C. O. (2018). Implicit hybrid points approach for solving general
second order ordinary differential equations with initial values. Journal of Advances in Mathematics and
Computer Science, 27(3), 1-14.
Kwari, L. J., Sunday, J., Ndam, J. N., Shokri, A., Wang, Y. (2023). On the simulations of second-order oscillatory
problems with applications to physical systems. Axioms, 12, 9, 10. https://doi.org/10.3390/axioms12030282
Arevalo, C., Soderlind, G., Hadjimichael, Y., Fekete, I. (2021). Local error estimation and step size control in
adaptative linear multistep methods. Numer. Algorithms, 86, 537-563.
Sabo, J. (2021). Single step block hybrid methods for direct solution of higher order initial value problems. M.Sc.
Thesis, Adamawa State University, Mubi-Nigeria. (Unpublished), 5-11.
Areo, E. A., Rufai, M. A. (2016). An efficient one-eight step hybrid block method for solving second order initial
value problems of ODEs. International Journal of Differential Equation and Application, 15(2), 117-139.
Skwame, Y., Donald, J. Z., Kyagya, T. Y., Sabo, J., Bambur, A. A. (2020). The numerical applications of implicit
second derivative on second order initial value problems of ordinary differential equations. Dutse Journal of Pure
and Applied Sciences, 6(4), 1-14.
Lydia, J. K., Joshua S. Ndam J. N., James, A. A. (2021). On the numerical approximations and simulations of
damped and undamped duffing oscillators. Science Forum (Journal of Pure and Applied Science), 21, 503-515.
Olabode, B. T., Momoh, A. L. (2016). Continuous hybrid multistep methods with Legendre basic function for
treatment of second order stiff ODEs. American Journal of Computational and Applied Mathematics, 6(2),
-49.
Jator, S. N., Li. (2009). A self-starting linear multistep method for the direct solution of a general second order
initial value problem. International Journal of Computer Math, 86(5), 817-836.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 International Journal of Development Mathematics (IJDM)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors are solely responsible for obtaining permission to reproduce any copyrighted material contained in the manuscript as submitted. Any instance of possible prior publication in any form must be disclosed at the time the manuscript is submitted and a
copy or link to the publication must be provided.
The Journal articles are open access and are distributed under the terms of the Creative
Commons Attribution-NonCommercial-NoDerivs 4.0 IGO License, which permits use,
distribution, and reproduction in any medium, provided the original work is properly cited.
No modifications or commercial use of the articles are permitted.
