New Analytical Approximations with Error Estimates for the One-loop Soliton Solution to the Vakhnenko Equation

DOI

10.2991/icence-16.2016.60How to use a DOI?

Keywords

Vakhnenko Equation; New Analytical Approximations; Error Estimate; Accuracy; Convergence Rate; Piecewise Perturbation Method

Abstract

In this paper, based on the traditional homotopy analysis method, we have successfully proposed a new analytical method, namely the piecewise perturbation method (PPM), for solving nonlinear problems. Here we introduce the idea of Newton iteration into the traditional homotopy analysis method to revise the initial guesses, which significantly increases the accuracy and the convergence rate of the series solutions. Further, we apply this method to obtain the one-loop soliton solution of the Vakhnenko equation in order to verify its potential and validity in solving nonlinear problems. With the aid of the optimal value of the convergence-control parameter determined by the averaged residual error technique, comparisons are made between the proposed method and the traditional homotopy analysis method. The results reveal that these new approximations with error estimates possess better accuracy and higher convergence rate than those obtained by the traditional homotopy analysis method.

Copyright

© 2016, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Yupeng Qin
AU  - Li Zou
AU  - Zhen Wang
AU  - Mingfeng He
PY  - 2016/09
DA  - 2016/09
TI  - New Analytical Approximations with Error Estimates for the One-loop Soliton Solution to the Vakhnenko Equation
BT  - Proceedings of the 2nd International Conference on Electronics, Network and Computer Engineering (ICENCE 2016)
PB  - Atlantis Press
SP  - 286
EP  - 297
SN  - 2352-538X
UR  - https://doi.org/10.2991/icence-16.2016.60
DO  - 10.2991/icence-16.2016.60
ID  - Qin2016/09
ER  -