Simulating the Dynamics of Oscillating Differential Equations of Mass in Motion

Авторы

  • Adewale A. James American University of Nigeria, Yola Автор
  • Sabo John Department of Mathematics, Faculty of Science, Adamawa State University, Mubi, Nigeria Автор

DOI:

https://doi.org/10.62054/ijdm/0101.07

Аннотация

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

Библиографические ссылки

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.

Опубликован

2024-03-20

Как цитировать

Simulating the Dynamics of Oscillating Differential Equations of Mass in Motion. (2024). International Journal of Development Mathematics (IJDM), 1(1). https://doi.org/10.62054/ijdm/0101.07