Volume 69 | Issue 2 | Year 2023 | Article Id. IJMTT-V69I2P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I2P512
Received | Revised | Accepted | Published |
---|---|---|---|
03 Jan 2023 | 07 Feb 2023 | 19 Feb 2023 | 28 Feb 2023 |
Enormous applications in real life and in engineering motivated this analysis that provides a report on present work. A Method of Differential Transforms (DTM) is applied on certain differential equations to get a semi analytic solution that helps in rectifying the critical gap that allows to improvise the results of differential equation model in numerous fields. The uniqueness of this paper proposes a succinct solution found with certain added features making the equations compatible, and are matched well with analytical, numerical approach and Laplace transform procedure.
[1] J.K. Zhou, “Differential Transformation and Its Applications for ElectricalCircuits,” Huazhong University Press, Wuhan, China, 1986.
[2] Tanfer Tanriverdi, and Nermin Ağırağaç, “Differential Transform Applied to certain ODE,” Advances in Differential Equations and Control Processes, vol. 19, no. 3, 2018, pp. 213-235, 2018. Crossref, http://dx.doi.org/10.17654/DE019030213
[3] Birol İbiş, “Approximate Analytical Solutions for Nonlinear Emden-Fowler type Equations by Differential Transform Method,” Mathematical Physics, 2012. Crossref, https://doi.org/10.48550/arXiv.1211.3521
[4] P.S. Sutkar, “Solution of Some Differential Equations by Using Differential Transform Method,” International Journal of Scientific and Innovative Mathematical Research (IJSIMR), vol. 5, no. 5, pp. 17-20, 2017. Crossref, http://dx.doi.org/10.20431/2347-3142.0505003
[5] Vedat Suat Ertürk, “Differential Transformation Method for Solving Differential Equations of Lane-Emden Type,” Mathematical and Computational Applications, vol. 12, no. 3, pp. 135-139, 2007. Crossref, https://doi.org/10.3390/mca12030135
[6] J. Biazar, and M. Elslami, “Differential Transform Method for Quadratic Ricatti Differential Equation,” International Journal of Nonlinear Science, vol. 9, no. 4, pp. 444-447, 2010.
[7] Javed Ali, “One Dimensional Differential Transform Method for Higher Order Boundary Value Problems in Finite Domain,” International Journal of Contemporary Mathematical Sciences, vol. 7, no. 6, pp. 263-272, 2012.
[8] Farshid Mirzaee, “Differential Transform Method for Solving Linear and Non-linear Systems of Differential Equations,” Applied Mathematical Sciences, vol. 5, no. 70, pp. 3465-3472, 2011.
[9] Hooman Fatoorehchi, Hoosein Abolghasemi, and Nanjundan Magesh, “The Differential Transform Method as a New Computational Tool for Laplace Transforms,” National Academy Science Letters, vol. 38, pp. 157–160. 2015. Crossref, https://doi.org/10.1007/s40009-014-0308-6
[10] Montri Thongmoon, and Sasitorn Pusjuso, “The Numerical Solutions of Differential Transform Method and The Laplace Transform Method for a System of Differential Equations,” Nonlinear Analysis: Hybrid Systems, vol. 4, no. 3, pp. 425-431, 2010. Crossref, https://doi.org/10.1016/j.nahs.2009.10.006
[11] Hooman Fatoorehchi, and Hossein Abolghasemi, “Computation of Analytical Laplace Transforms by the Differential Transform Method,” Mathematical and Computer Modelling, vol. 56, no. 7-8, pp. 145-151, 2012. Crossref, https://doi.org/10.1016/j.mcm.2011.11.063
[12] O.D. Ogwumu et al., “Differential Transform Method (DTM) for the Solution of Linear Ordinary Differential Equations of First Order, Second Order and Third Order,” International Journal of Research and Innovation in Applied Science, vol. V, no. II, pp. 25-30, 2020.
[13] Narhari Onkar Warade, and Prabha Rastogi, “Application to Differential Transformation Method for Solving Eight Order Ordinary Differential Equations,” International Journal of Mathematics Trends and Technology, vol. 61, no. 3, pp. 177-185, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V61P525
[14] Yogeshwari Patel, and Jayesh M. Dhodiya, “Differential Transform Method to Solve Linear and Non Linear Diffusion Equation,” International Journal of Mathematics Trends and Technology (IJMTT), vol. 33, no. 1, pp. 1-4, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V33P501
[15] Narhari Onkar Warade, and Prabha Rastogi, “Application of Zhou’s Method for Solving Oscillation and Euler’s Differential Equations,” International Journal of Mathematics Trends and Technology (IJMTT), vol. 56, no. 4, pp. 289-293, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V56P539
[16] S.Padmasekaran, and C.Thangavelu, “The (n + 1) Dimensional Equal Width Wave Equation by differential transform method,” International Journal of Mathematics Trends and Technology (IJMTT), vol. 63, no. 2, pp. 109-117, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V63P514
[17] Rahul Bhadauria, A.K. Singh, and D.P Singh, “A Mathematical Model to Solve Reaction Diffusion Equation using Differential Transformation Method,” International Journal of Mathematics Trends and Technology, vol. 2, no. 2, pp. 26-31, 2011.
[18] DibyenduSaha, and SanjibSengupta, “A Comparative Analysis of DTM and HAM Solutions for Hunter-Saxton Equation and Fisher Equation,” International Journal of Mathematics Trends and Technology (IJMTT), vol. 56, no. 4, pp. 236-243, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V56P534
[19] R.N Prajapati, Rakesh Mohan, and Pankaj Kumar, “Fractional Order Hirota-Satsuma Coupled KdV Equation by Homotopy Perturbation Transforms Method,” International Journal of Mathematics Trends and Technology (IJMTT), vol. 33, no. 3, pp. 148-155, 2016.
[20] S.Padmasekaran, R.Asokan, and K.Alaguraja, “An Analytical Solution of (2+1)-Dimensional Equal width Wave Equation with Diffusivity by HPM, ADM and DTM,” International Journal of Mathematics Trends and Technology (IJMTT), vol. 56, no. 1, pp. 40-49, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V56P506
[21] Narhari Onkar Warade, and Prabha Rastogi, “Zhou’s Differential Transformation Method for Study of Arm Race Richardson Model,” International Journal of Mathematics Trends and Technology (IJMTT), vol. 57, no. 6, pp. 382-387, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V57P552
[22] Somayeh Abbasi, Fatemeh Farhatnia, and Saeid Rasouli Jazi, “Application of Differential Transformation Method (DTM) for Bending Analysis of Functionally Graded Circular Plates,” Caspian Journal of Applied Sciences Research, vol. 2, no. 4, pp. 17-23, 2013.
[23] Narhari Onkar Warade, and Prabha Rastogi, “Application to Differential Transformation Method for Solving Eight Order Ordinary Differential Equations,” International Journal of Mathematics Trends and Technology, vol. 61, no. 3, pp. 177-185, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V61P525
[24] S.Karunanithi et al., “A Study on Comparison of Jacobi, Gauss-Seidel and Sor Methods for the Solution in System of Linear Equations,” International Journal of Mathematics Trends and Technology (IJMTT), vol. 56, no. 4, pp. 214-222, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V56P531
[25] Liberty Ebiwareme, “Application of Semi-Analytical Iteration Techniques for the Numerical Solution of Linear and Nonlinear Differential Equations,” International Journal of Mathematics Trends and Technology, vol. 67, no. 2, pp. 146-158, 2021. Crossref, https://www.ijmttjournal.org/archive/ijmtt-v67i2p521
H. R. Swathi, T. C. Sushma, "DTM Approach on Certain Differential Equations in Real Life Applications," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 2, pp. 91-97, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I2P512