For EDITORS

For READERS

All Issues

Vol.15, 2025
Vol.14, 2024
Vol.10, 2020
Vol.9, 2019
Vol.8, 2018
Vol.7, 2017
Vol.6, 2016
Vol.5, 2015
Vol.4, 2014
Vol.3, 2013
Vol.2, 2012
Vol.1, 2011
Volume 6, Number 1, 2016, Pages 103-118                                                                DOI:10.11948/2016009
An optimal homotopy analysis method based on particle swarm optimization: application to fractional-order differential equation
Li-Guo Yuan,Zeeshan Alam
Keywords:Optimal homotopy analysis method  particle swarm optimization  fractional-order differential equation  Caputo derivative  residual error.
Abstract:
      This paper describes a new problem-solving mentality of finding optimal parameters in optimal homotopy analysis method (optimal HAM). We use particle swarm optimization (PSO) to minimize the exact square residual error in optimal HAM. All optimal convergence-control parameters can be found concurrently. This method can deal with optimal HAM which has finite convergence-control parameters. Two nonlinear fractional-order differential equations are given to illustrate the proposed algorithm. The comparison reveals that optimal HAM combined with PSO is effective and reliable. Meanwhile, we give a sufficient condition for convergence of the optimal HAM for solving fractional-order equation, and try to put forward a new calculation method for the residual error.
PDF      Download reader