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Mbagwu, Johnpaul, Tunç, Cemil, Enjoh, Chris, Onwuemekaa, J.I.. (1400). Solving second order ordinary differential equations by using Newton’s interpolation and Aitken’s methods. نشریه هنرهای کاربردی, 13(1), 1057-1066. doi: 10.22075/ijnaa.2021.24027.2657
Johnpaul Chiagoziem Mbagwu; Cemil Tunç; Chris Enjoh; J.I. Onwuemekaa. "Solving second order ordinary differential equations by using Newton’s interpolation and Aitken’s methods". نشریه هنرهای کاربردی, 13, 1, 1400, 1057-1066. doi: 10.22075/ijnaa.2021.24027.2657
Mbagwu, Johnpaul, Tunç, Cemil, Enjoh, Chris, Onwuemekaa, J.I.. (1400). 'Solving second order ordinary differential equations by using Newton’s interpolation and Aitken’s methods', نشریه هنرهای کاربردی, 13(1), pp. 1057-1066. doi: 10.22075/ijnaa.2021.24027.2657
Mbagwu, Johnpaul, Tunç, Cemil, Enjoh, Chris, Onwuemekaa, J.I.. Solving second order ordinary differential equations by using Newton’s interpolation and Aitken’s methods. نشریه هنرهای کاربردی, 1400; 13(1): 1057-1066. doi: 10.22075/ijnaa.2021.24027.2657

Solving second order ordinary differential equations by using Newton’s interpolation and Aitken’s methods

International Journal of Nonlinear Analysis and Applications
مقاله 88، دوره 13، شماره 1، خرداد 2022، صفحه 1057-1066    اصل مقاله (395.54 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.24027.2657
نویسندگان
Johnpaul Chiagoziem Mbagwu* 1؛ Cemil Tunç2؛ Chris Enjoh3؛ J.I. Onwuemekaa1
1Department of Physics, Faculty of Physical Science, Imo State University, Owerri, Nigeria.
2Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University 65080, Van-Turkey
3Group Research in Analytical Chemistry, Environment and Climate Change (GRACE\&CC), Department of Chemistry, Faculty of Physical Science, Imo State University, Owerri, Nigeria
تاریخ دریافت: 29 تیر 1400،  تاریخ بازنگری: 10 شهریور 1400،  تاریخ پذیرش: 05 آبان 1400 
چکیده
In this paper, the methods called Newton’s interpolation and Aitken’s methods were developed and examined. We use Newton’s interpolation and Aitken’s methods to find the exact and analytic results for three different types of nonlinear ordinary differential equations (NLODEs) of first and second order through illustrative examples. By using the new method, we successfully handle some class of nonlinear ordinary differential equations of first and second order in a simple and elegant way compared to Newton’s and Lagrange methods in previous studies. One can conclude that Newton’s interpolation and Aitken’s methods are easy to yield and implement actual precise results.
کلیدواژه‌ها
Ordinary differential equation؛ Newton’s interpolation method؛ Aitken’s method
مراجع

[1] M. A. Al-Jawary, M. I. Adwan and G. H. Radhi, Three iterative methods for solving second order nonlinear ODEs arising in physics, J. King Saud Univ. Sci., 32 (2020) 312–323.

[2] S. Cuneyt, Numerical methods interpolation, Mech. Eng. Department Middle East Technical University Ankara, Turkey, 2004.

[3] P.J. Davis, Interpolation and approximation, Second edition, Dover, New York, NY, 1975.

[4] I.N. Din, Using Newton’s interpolation and Aitken’s method for solving first order differential equation, World Appl. Sci. J., 38 (2020) 191-194.

[5] C.K. Faith, Solution of first-order differential equation using numerical Newton’s interpolation and Lagrange method, Int. J. Dev. Res. , 8 (2018) 18973-18976.

[6] H. Fatoorehchi, and H. Abolghasemi, Series solution of nonlinear differential equations by a novel extension of the Laplace transform method, Int. J. Comput. Math., 93 (2016) 1299-1319.

[7] E. Isaacson and H.B. Keller, Numerical Analysis and numerical methods, Second edition, PWS-KENT Publishing NY, 1994.

[8] M. E. Islama and M. A. Akbarb, Stable wave solutions to the Landau-Ginzburg-Higgs equation and the modified equal width wave equation using the IBSEF method, Arab J. Basic Appl. Sci., 27 (2020) 270–278.

[9] S. R. Mahmoud and M. Shehu, Solving nonlinear ordinary differential equations using the NDM, J. Appl. Anal. Comput. , 5 (2015), 77-88.

[10] JP.C. Mbagwu, B. I. Madububa and J. I. Nwamba, Series solution of nonlinear ordinary differential equations using single Laplace transform method in mathematical physics, World Scientific News, 154 (2021) 152-174.

[11] S. Mesbahi, Existence result of solutions for a class of nonlinear differential system, Int. J. Nonlinear Anal. Appl., 12 (2021) 1-10.

[12] L. B. Richard and J. D. Faires, Numerical Analysis, PWS-KENT Publishing Company, Boston, 1989.

[13] J. Stoer and R. Burlisch, Introduction to numerical analysis, Second edition, Springer-Verlag, New York, NY, 1993.

[14] H. Temimi and A. R. Ansari, A new iterative technique for solving nonlinear second order multi-point boundary value problems, Appl. Math. Comput., 218 (2011) 1457–1466.

[15] O. Tun¸c, C. Tun¸c, On the boundedness and integration of non-oscillatory solutions of certain linear differential equations of second order, J. Adv. Res., 7 165-168, https://doi.org/10.1016/j.jare.2015.04.005(1) (2016).

[16] O. Tun¸c, C. Tun¸c, A note on certain qualitative properties of a second order linear differential system, Appl. Math. Inf. Sci., 9(2) (2015) 953-956,https://doi.org/10.12785/amis/090245.

[17] O. Tun¸c, C. Tun¸c, On the asymptotic stability of solutions of stochastic differential delay equations of second order, J. Taibah Univ. Sci., 13(1) (2019) 875–882,https://doi.org/10.1080/16583655.2019.1652453.

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