The new modified Ishikawa iteration method for the approximate solution of different types of differential equations

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Bildik N., Bakir Y., MUTLU A.

Fixed Point Theory and Applications, cilt.2013, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2013
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1186/1687-1812-2013-52
  • Dergi Adı: Fixed Point Theory and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: ordinary differential equation, Euler method, fixed point, numerical analysis, modified Ishikawa iteration, Picard successive iteration method
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

In this article, the new Ishikawa iteration method is presented to find the approximate solution of an ordinary differential equation with an initial condition. Additionally, some numerical examples with initial conditions are given to show the properties of the iteration method. Furthermore, the results of absolute errors are compared with Euler, Runge-Kutta and Picard iteration methods. Finally, the present method, namely the new modified Ishikawa iteration method, is seen to be very effective and efficient in solving different type of the problem. © 2013 Bildik et al.; licensee Springer.