A short review on approximate analytical methods for non-linear problems-Reference-Cited by-同舟云学术

A short review on approximate analytical methods for non-linear problems

Published:2022 Issue:3 Part B Volume:26 Page:2607-2618
ISSN:0354-9836
Container-title:Thermal Science
language:en
Short-container-title:THERM SCI

Author:

Tian Yi¹,Feng Guang-Qing²

Affiliation:

1. College of Data Science and Application, Inner Mongolia University of Technology, Hohhot, China

2. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, China

Abstract

In this paper, some approximate analytical methods are reviewed, including the variational iteration method and the homotopy perturbation method. Based on the ideas of the two methods, a new method for solving a class of system of Fredholm integral equations of the second kind is proposed. Some examples are given to show the simple solution process and the accuracy of the solution for each method. The emphasis of this review paper focuses on Ji-Huan He?s unapproachable ideas and the mathematics beauty, so the references are not exhaustive.

Publisher

National Library of Serbia

Subject

Renewable Energy, Sustainability and the Environment

Reference46 articles.

1. He, J.-H. Homotopy Perturbation Technique, Computer Methods in Applied Mechanics and Engineering, 178 (1999), 3-4, pp. 257-262

2. He, J.-H., Variational Iteration Method-a Kind of Non-Linear Analytical Technique: Some Examples, International Journal of Non-linear Mechanics, 34 (1999), 4, pp. 699-708

3. He, J.-H., Taylor Series Solution for a Third Order Boundary Value Problem Arising in Architectural Engineering, Ain Shams Engineering Journal, 11 (2020), 4, pp. 1411-1414

4. He, J.-H., Wu, X. H., Exp-Function Method for Non-Linear Wave Equations, Chaos Solitons & Fractals, 30 (2006), 3, pp. 700-708

5. He, J.-H., Exp-Function Method for Fractional Differential Equations, International Journal of Non-linear Sciences and Numerical Simulation, 14 (2013), 6, pp. 363-366

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