Modified differential transform scheme for solving systems of first order ordinary differential equations
-
1446
Downloads
-
3237
Views
Authors
S. Al-Ahmad
- Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Terengganu, Besut Campus, 22200, Malaysia.
I. M. Sulaiman
- Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Terengganu, Besut Campus, 22200, Malaysia.
M. Mamat
- Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Terengganu, Besut Campus, 22200, Malaysia.
Puspa Liza Ghazali
- Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Terengganu, Besut Campus, 22200, Malaysia.
Abstract
In this paper, a modified differential transform scheme (MDTS) is proposed for solving systems of first order ordinary differential equations. This numerical scheme serves as an alternative approach that is designed based on the differential transform method (DTM), Laplace transform and Pade approximants. The proposed method would be able to overcome the difficulty of solving these types of problems and also, gives a virtuous approximation for the true solution of the problems in a large region. Preliminary results are presented based on some examples which illustrate the validity and applicability of the proposed scheme. Also, all the obtained results corresponded to exact solutions.
Share and Cite
ISRP Style
S. Al-Ahmad, I. M. Sulaiman, M. Mamat, Puspa Liza Ghazali, Modified differential transform scheme for solving systems of first order ordinary differential equations, Journal of Mathematics and Computer Science, 22 (2021), no. 1, 73--84
AMA Style
Al-Ahmad S., Sulaiman I. M., Mamat M., Ghazali Puspa Liza, Modified differential transform scheme for solving systems of first order ordinary differential equations. J Math Comput SCI-JM. (2021); 22(1):73--84
Chicago/Turabian Style
Al-Ahmad, S., Sulaiman, I. M., Mamat, M., Ghazali, Puspa Liza. "Modified differential transform scheme for solving systems of first order ordinary differential equations." Journal of Mathematics and Computer Science, 22, no. 1 (2021): 73--84
Keywords
- Systems of first order ordinary differential equations
- differential transform method
- Laplace transform
- Pade approximants
MSC
References
-
[1]
S. Al-Ahmad, M. Mamat, R. Al-Ahmad, Finding Differential Transform Using Difference Equations, IAENG Int. J. Appl. Math., 50 (2020), 127--132
-
[2]
S. Al-Ahmad, M. Mamat, R. Al-Ahmad, I. M. Sulaiman, P. L. Ghazali, M. A. Mohamed, On New Properties of Differential Transform via Difference Equations, Int. J. Eng. Tech., 7 (2018), 321--324
-
[3]
A. H. Ali, Applications of Differential Transform Method To Initial Value Problems, Amer. J. Eng. Res., 6 (2017), 365--371
-
[4]
A. K. Alomari, N. Ratib Anakira, A. S. Bataineh, I. Hashim, Approximate solution of nonlinear system of BVP arising in fluid flow problem, Math. Probl. Eng., 2013 (2013), 7 pages
-
[5]
N. Anakira, Solution of system of ordinary differential equations by optimal homotopy asymptotic method, AIP Conference Proceedings, 2096 (2019), 5 pages
-
[6]
F. Ayaz, Solutions of the system of differential equations by differential transform method, Appl. Math. Comput., 147 (2004), 547--567
-
[7]
G. A. Baker, Essentials of Padé approximants, Academic Press, London (1975)
-
[8]
C. M. Bender, S. A. Orszag, Advanced mathematical methods for scientists and engineers I: Asymptotic methods and perturbation theory, Springer, New York (2013)
-
[9]
J. Biazar, E. Babolian, R. Islam, Solution of the system of ordinary differential equations by Adomian decomposition method, Appl. Math. Comput., 147 (2004), 713--719
-
[10]
J. Biazar, H. Ghazvini, He's variational iteration method for solving linear and non-linear systems of ordinary differential equations, Appl. Math. Comput., 191 (2007), 287--297
-
[11]
C.-L. Chen, S.-H. Lin, C.-K. Chen, Application of Taylor transformation to nonlinear predictive control problem, Appl. Math. Modelling, 20 (1996), 699--710
-
[12]
B. Ibis, Approximate analytical solutions for nonlinear Emden-Fowler type equations by differential transform method, arXiv, 2012 (2012), 7 pages
-
[13]
A. F. Jameel, N. R. Anakira, M. M. Rashidi, A. K. Alomari, A. Saaban, M. A. Shakhatreh, Differential Transformation Method For Solving High Order Fuzzy Initial Value Problems, Ital. J. Pure Appl. Math., 39 (2018), 194--208
-
[14]
F. Mirzaee, Differential Transform Method for Solving Linear and Nonlinear Systems of Ordinary Differential Equations, Appl. Math. Sci. (Ruse), 5 (2011), 3465--3472
-
[15]
S. Momani, V. S. Ertürk, Solutions of non-linear oscillators by the modified differential transform method, Comput. Math. Appl., 55 (2008), 833--842
-
[16]
Z. M. Odibat, Differential transform method for solvin Volterra integral equation with separable kernels, Math. Comput. Modelling, 48 (2008), 1144--1149
-
[17]
A. S. V. Ravi Kanth, K. Aruna, Differential transform method for solving linear and non-linear systems of partial differential equations, Phys. Lett. A, 372 (2008), 6896--6898
-
[18]
M. Thongmoon, S. Pusjuso, The numerical solutions of differential transform method and the Laplace transform method for a system of differential equations, Nonlinear Anal. Hybrid Syst., 4 (2010), 425--431
-
[19]
J. K. Zhou, Differential transformation and Application for electrical circuits, Huazhong University Press, Wuhan (1986)