Review of the new perturbation-iteration method

Pakdemirli M.

Mathematical and Computational Applications, vol.18, no.3, pp.139-151, 2013 (Scopus, TRDizin) identifier

  • Publication Type: Article / Review
  • Volume: 18 Issue: 3
  • Publication Date: 2013
  • Doi Number: 10.3390/mca18030139
  • Journal Name: Mathematical and Computational Applications
  • Journal Indexes: Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.139-151
  • Keywords: Algebraic equations, Integral equations, Ordinary differential equations, Perturbation method, Perturbation-iteration algorithm
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

The new perturbation iteration method developed by Pakdemirli and co-workers are reviewed. First, applications of the method to algebraic equations are discussed and some new root-finding algorithms developed by this method are given. Next, the applications of the new method to first order, second order and systems of first order ordinary differential equations are discussed. Three sample problems are selected. Results are compared with analytical solutions, solutions by other methods and numerical solutions. The new perturbation iteration method is an effective method that does not require small parameter assumption as in classical perturbation methods.