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Hadian Rasanan, Amir Hosein, Nikarya, Mehran, Moayeri, Mohammad Mahdi, Bahramnezhad, Arman. (1401). A comparison between pre-Newton and post-Newton approaches for solving a physical singular second-order boundary problem in the semi-infinite interval. , 1(1), 116-125. doi: 10.52547/CMCMA.1.1.116
Amir Hosein Hadian Rasanan; Mehran Nikarya; Mohammad Mahdi Moayeri; Arman Bahramnezhad. "A comparison between pre-Newton and post-Newton approaches for solving a physical singular second-order boundary problem in the semi-infinite interval". , 1, 1, 1401, 116-125. doi: 10.52547/CMCMA.1.1.116
Hadian Rasanan, Amir Hosein, Nikarya, Mehran, Moayeri, Mohammad Mahdi, Bahramnezhad, Arman. (1401). 'A comparison between pre-Newton and post-Newton approaches for solving a physical singular second-order boundary problem in the semi-infinite interval', , 1(1), pp. 116-125. doi: 10.52547/CMCMA.1.1.116
Hadian Rasanan, Amir Hosein, Nikarya, Mehran, Moayeri, Mohammad Mahdi, Bahramnezhad, Arman. A comparison between pre-Newton and post-Newton approaches for solving a physical singular second-order boundary problem in the semi-infinite interval. , 1401; 1(1): 116-125. doi: 10.52547/CMCMA.1.1.116

A comparison between pre-Newton and post-Newton approaches for solving a physical singular second-order boundary problem in the semi-infinite interval

Computational Mathematics and Computer Modeling with Applications (CMCMA)
دوره 1، شماره 1، شهریور 2022، صفحه 116-125    اصل مقاله (225.08 K)
نوع مقاله: Regular paper
شناسه دیجیتال (DOI): 10.52547/CMCMA.1.1.116
نویسندگان
Amir Hosein Hadian Rasanan* 1؛ Mehran Nikarya2؛ Mohammad Mahdi Moayeri3؛ Arman Bahramnezhad4
1School of Computer Science, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
2Department of Electrical Engineering and Information Technology, Iranian Research Organization for Science and Technology (IROST), Tehran, Iran
3Department of Computer and Data Sciences, Shahid Beheshti University, Tehran, Iran.
4Department of Computer and Data Sciences, Shahid Beheshti University, Tehran, Iran
چکیده
In this paper, two numerical approaches based on the Newton iteration method with spectral algorithms are introduced to solve the Thomas-Fermi equation. That Thomas-Fermi equation is a nonlinear singular ordinary differential equation (ODE) with a boundary condition in infinite. In these schemes, the Newton method is combined with a spectral method where in one of those, by the Newton method we convert nonlinear ODE to a sequence of linear ODE and then, solve them using the spectral method. In another one, by the spectral method, the nonlinear ODE is converted to a system of nonlinear algebraic equations, then, this system is solved by the Newton method. In both approaches, the spectral method is based on the fractional order of rational Gegenbauer functions. Finally, the obtained results of the two introduced schemes are compared to each other in accuracy, runtime, and iteration number. Numerical experiments are presented showing that our methods are as accurate as the best results obtained until now.
کلیدواژه‌ها
Pre-Newton method؛ Post-Newton method؛ Fractional order of rational Gegenbauer functions؛ Thomas-Fermi equation؛ Spectral method
آمار
تعداد مشاهده مقاله: 48
تعداد دریافت فایل اصل مقاله: 53