Modelling Taylor's Table Method for Numerical Differentiation in Python
Автор: Pankaj Dumka, Rishika Chauhan, Dhananjay R. Mishra
Журнал: International Journal of Mathematical Sciences and Computing @ijmsc
Статья в выпуске: 4 vol.9, 2023 года.
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In this article, an attempt has been made to explain and model the Taylor table method in Python. A step-by-step algorithm has been developed, and the methodology has been presented for programming. The developed TT_method() function has been tested with the help of four problems, and accurate results have been obtained. The developed function can handle any number of stencils and is capable of producing the results instantaneously. This will eliminate the task of hand calculations and the use can directly focus on the problem solving rather than working hours to descretize the problem.
Taylor's Table method, Applications in numerical differentiation, Simulations in Python programming
Короткий адрес: https://sciup.org/15019065
IDR: 15019065 | DOI: 10.5815/ijmsc.2023.04.03
Список литературы Modelling Taylor's Table Method for Numerical Differentiation in Python
- R.A. Usmani, P.J. Taylor, Finite Difference Methods for Solving, Int. J. Comput. Math. 14 (1983) 277–293. https://doi.org/10.1080/00207168308803391.
- J.F. Epperson, An introduction to numerical methods and analysis, John Wiley \& Sons, 2021. https://doi.org/10.1002/9781119604754.
- P. Dumka, R. Dumka, D.R. Mishra, Numerical Methods Using Python, BlueRose, 2022.
- B. Hashemi, Y. Nakatsukasa, Least-squares spectral methods for ODE eigenvalue problems, (2021). http://arxiv.org/abs/2109.05384.
- P.S. Pawar, D.R. Mishra, P. Dumka, Solving First Order Ordinary Differential Equations using Least Square Method?: A comparative study, Int. J. Innov. Sci. Res. Technol. 7 (2022) 857–864.
- R. Anderssen, M. Hegland, For numerical differentiation, dimensionality can be a blessing!, Math. Comput. 68 (1999) 1121–1141. https://doi.org/10.1090/s0025-5718-99-01033-9.
- V. T., J.C. Strikwerda, Finite Difference Schemes and Partial Differential Equations., SIAM, 1990. https://doi.org/10.2307/2008454.
- A. Marowka, On parallel software engineering education using python, Educ. Inf. Technol. 23 (2018) 357–372. https://doi.org/10.1007/s10639-017-9607-0.
- P. Dumka, R. Chauhan, A. Singh, G. Singh, D. Mishra, Implementation of Buckingham ’ s Pi theorem using Python, Adv. Eng. Softw. 173 (2022) 103232. https://doi.org/10.1016/j.advengsoft.2022.103232.
- P. Dumka, K. Rana, S. Pratap, S. Tomar, P.S. Pawar, D.R. Mishra, Modelling air standard thermodynamic cycles using python, Adv. Eng. Softw. 172 (2022) 103186. https://doi.org/10.1016/j.advengsoft.2022.103186.
- J.W.B. Lin, Why python is the next wave in earth sciences computing, Bull. Am. Meteorol. Soc. 93 (2012) 1823–1824. https://doi.org/10.1175/BAMS-D-12-00148.1.
- R. Johansson, Numerical python: Scientific computing and data science applications with numpy, SciPy and matplotlib, Second edition, Apress, Berkeley, CA, 2018. https://doi.org/10.1007/978-1-4842-4246-9.
- C. Fuhrer, O. Verdier, J.E. Solem, C. Führer, O. Verdier, J.E. Solem, Scientific Computing with Python. High-performance scientific computing with NumPy, SciPy, and pandas, Packt Publishing Ltd, 2021.
- A. Meurer, C.P. Smith, M. Paprocki, O. ?ertík, S.B. Kirpichev, M. Rocklin, Am.T. Kumar, S. Ivanov, J.K. Moore, S. Singh, T. Rathnayake, S. Vig, B.E. Granger, R.P. Muller, F. Bonazzi, H. Gupta, S. Vats, F. Johansson, F. Pedregosa, M.J. Curry, A.R. Terrel, Š. Rou?ka, A. Saboo, I. Fernando, S. Kulal, R. Cimrman, A. Scopatz, SymPy: Symbolic computing in python, PeerJ Comput. Sci. 2017 (2017) 1–27. https://doi.org/10.7717/peerj-cs.103.
- P. Dumka, P.S. Pawar, A. Sauda, G. Shukla, D.R. Mishra, Application of He’s homotopy and perturbation method to solve heat transfer equations: A python approach, Adv. Eng. Softw. 170 (2022) 103160. https://doi.org/10.1016/j.advengsoft.2022.103160.
