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

Mbagwu J. P. C., Tunç C., Enyoh C. E., Onwuemekaa J. I.

INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, cilt.13, sa.1, ss.1057-1066, 2022 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.22075/ijnaa.2021.24027.2657
  • Dergi Adı: INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.1057-1066
  • Anahtar Kelimeler: Ordinary differential equations, Newton's interpolation method, Aitken's method
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

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.