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Math. Comput. Appl. 2013, 18(3), 139-151; doi:10.3390/mca18030139

Review of the New Perturbation-Iteration Method

Department of Mechanical Engineering, Celal Bayar University 45140, Muradiye, Manisa Turkey
Published: 1 December 2013
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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.
Keywords: perturbation method; perturbation-iteration algorithm; algebraic equations; ordinary differential equations; integral equations perturbation method; perturbation-iteration algorithm; algebraic equations; ordinary differential equations; integral equations
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Pakdemirli, M. Review of the New Perturbation-Iteration Method. Math. Comput. Appl. 2013, 18, 139-151.

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