Abstract
In this research, a semi-analytical solution called differential transformation method (DTM) was used to solve the Lane-Emden equation. With the help of Maple 2020, the approximate solutions of the Lane-Emden equation were obtained. The numerical result derived by DTM is compared with the result of Adomian decomposition method (ADM), Legendre wavelets and Homotopy perturbation method with Laplace transformation (LT-HPM) which were done by previous research to observe the accuracy of the value with the exact value. After comparing between the methods, the result represents the close approximation of DTM for solving Lane-Emden equation depending on the type of Lane-Emden equation and number of terms in DTM. For solving Lane-Emden equation, a few terms of DTM are recommended to obtain the approximate value. DTM has successfully solved three examples. Due to less computational work to obtain an approximation to exact value, DTM is considered to be the simplest method to apply and can solve differential problem.
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Aris Izzuddin Razali, M., Azliza Abd Latif, N. (2023). Solving Lane-Emden Equation by Using Differential Transformation Method. In: Mustapha, A., Ibrahim, N., Basri, H., Rusiman, M.S., Zuhaib Haider Rizvi, S. (eds) Proceedings of the 8th International Conference on the Applications of Science and Mathematics. EduTA 2022. Springer Proceedings in Physics, vol 294. Springer, Singapore. https://doi.org/10.1007/978-981-99-2850-7_1
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DOI: https://doi.org/10.1007/978-981-99-2850-7_1
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