IMPROVING α-PARAMETERIZED DIFFERENTIAL TRANSFORM METHOD WITH DANDELION OPTIMIZER FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS
Mustafa Raed Najeeb
mostafa.csp115@student.uomosul.edu.iqUniversity of Mosul, Mathematics Department (Iraq)
https://orcid.org/0000-0001-5471-7494
Omar Saber Qasim
University of Mosul, Mathematics Department (Iraq)
https://orcid.org/0000-0003-3301-6271
Abstract
In this manuscript, we aim to address Ordinary Differential Equations (ODEs) by α-Parameterized Differential Transform Method (α-PDTM). Additionally, we seek to enhance the effectiveness of α-PDTM by incorporating the Dandelion Optimizer (DO). The DO plays a crucial role in optimizing the parameter α, ensuring its adjustment and modification to secure the most favorable value. This refinement results in a more accurate approximation compared to conventional methods. The proposed approach, referred to as (αDO-PDTM), demonstrates a solution distinguished by its reliability and efficiency, as determined through the computation of Maximum Absolute Error (MAE) and the Mean Square Errors (MSE).
Keywords:
α-parameterized differential transform, Dandelion optimizer, ordinary differential equations, meta heuristicReferences
[1] Abd Elaziz M., Ewees A. A., Oliva D.: Hyper-heuristic method for multilevel thresholding image segmentation. Expert Systems with Applications 146, 2020, 113201.
Google Scholar
[2] Beheshti Z., Shamsuddin S. M. H.: A review of population-based meta-heuristic algorithms. Int. J. Adv. Soft Comput. Appl. 5(1), 2013, 1–35.
Google Scholar
[3] Doha E., Bhrawy A., Saker M.: On the derivatives of Bernstein polynomials: an application for the solution of high even-order differential equations. Boundary Value Problems 2011, 2011, 829543.
Google Scholar
[4] Mukhtarov O., Yücel M., Aydemir K.: A new generalization of the differential transform method for solving boundary value problems. Journal of New Results in Science 10(2), 2021, 49–58.
Google Scholar
[5] Murad M. A. S.: Modified integral equation combined with the decomposition method for time fractional differential equations with variable coefficients. Applied Mathematics-A Journal of Chinese Universities 37(3), 2022, 404-414.
Google Scholar
[6] Najeeb M. R., Entesar A., Qasim O. S.: Improving homotopy analytical method with sine cosine algorithm and Simpson integrative method for solving fractional ordinary differential equations. AIP Conference Proceedings 2398(1), 2022.
Google Scholar
[7] Qasim O. S., Entesar A.: Solve differential equations via a hybrid method between homotopy analytical method and sine cosine optimization algorithm. Journal of Physics: Conference Series 1879(3), 2021, 032048.
Google Scholar
[8] Shijun L.: Advances in the Homotopy Analysis Method. World Scientific, 2013.
Google Scholar
[9] Wang F., Yuan X., Liew S. C., Guo D.: Wireless MIMO switching: Weighted sum mean square error and sum rate optimization. IEEE Transactions on Information Theory 59(9), 2013, 5297–5312.
Google Scholar
[10] Wang Z., Li Y., Zhang H., Liu C., Chen Q.: Sampling-based optimal motion planning with smart exploration and exploitation. IEEE/ASME Transactions on Mechatronics 25(5), 2020, 2376–2386.
Google Scholar
[11] Wang Z., Yu F., Wang D., Liu T., Hu R.: Multi-threshold segmentation of breast cancer images based on improved dandelion optimization algorithm. The Journal of Supercomputing 80(3), 2023, 3849–3874.
Google Scholar
[12] Yücel M., Muhtarov F.: Parameterized Differential Transform Method and Its Application to Boundary Value Transmission Problems. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 28(2), 2023, 431–442.
Google Scholar
[13] Zhao S., Zhang T., Ma S., Chen M.: Dandelion Optimizer: A nature-inspired metaheuristic algorithm for engineering applications. Engineering Applications of Artificial Intelligence 114, 2022, 105075.
Google Scholar
[14] Zhou J.: Differential Transformation and Its Applications for Electronic Circuits. Huazhong Science & Technology University Press, China 1986.
Google Scholar
Authors
Mustafa Raed Najeebmostafa.csp115@student.uomosul.edu.iq
University of Mosul, Mathematics Department Iraq
https://orcid.org/0000-0001-5471-7494
Authors
Omar Saber QasimUniversity of Mosul, Mathematics Department Iraq
https://orcid.org/0000-0003-3301-6271
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