Who invented homotopy perturbation method?

Liao Shijun
The HAM was first devised in 1992 by Liao Shijun of Shanghai Jiaotong University in his PhD dissertation and further modified in 1997 to introduce a non-zero auxiliary parameter, referred to as the convergence-control parameter, c0, to construct a homotopy on a differential system in general form.

Why do we use homotopy analysis?

More importantly, unlike all perturbation and traditional non-perturbation methods, the homotopy analysis method provides us with both the freedom to choose proper base functions for approximating a nonlinear problem and a simple way to ensure the convergence of the solution series.

Who introduced homotopy?

Professor Shijun Liao
4.1 Introduction The homotopy analysis method (HAM), developed by Professor Shijun Liao (1992, 2012), is a powerful mathematical tool for solving nonlinear problems.

What is Helmholtz and Gibbs function?

The Gibbs–Helmholtz equation is a thermodynamic equation used for calculating changes in the Gibbs free energy of a system as a function of temperature. It was originally presented in an 1882 paper entitled “Die Thermodynamik chemischer Vorgange” by Hermann von Helmholtz.

What is the Helmholtz problem?

In mathematics, the eigenvalue problem for the Laplace operator is known as the Helmholtz equation. It corresponds to the linear partial differential equation. where ∇2 is the Laplace operator (or “Laplacian”), k2 is the eigenvalue, and f is the (eigen)function.

What is Lagrange multiplier in variational iteration method?

The Lagrange multiplier technique [1] was widely used to solve a number of nonlinear problems which arise in mathematical physics and other related areas, and it was developed into a powerful analytical method, i.e., the variational iteration method [2, 3] for solving differential equations.

Who proposed variational iteration method?

Ji-Huan He
Ji-Huan He first applied the variational iteration method to fractional differential equations [2], revealing a great success.

What is the formula of Del G?

ΔG=ΔG0+RTlnQ where Q is the ratio of concentrations (or activities) of the products divided by the reactants. Under standard conditions Q=1 and ΔG=ΔG0 . Under equilibrium conditions, Q=K and ΔG=0 so ΔG0=−RTlnK .

What is homotopy perturbation?

He’s Homotopy perturbation method suggested in this article is an efficient method for obtaining the most accurate solution of a highly nonlinear partial differential equation with initial condition.

Can the homotopy perturbation method be used for non-local boundary value problems?

 Abstract— In this paper, initial boundary value problems with non local boundary conditions are presented. The homotopy perturbation method (HPM) is used for solving linear and non linear initial boundary value problems with non classical conditions.

What is the perturbation technique?

The perturbation technique is one of the analytical methods to solve non-linear differential equations. This technique is widely used by engineers to solve some practical problems. Most often we obtain many interesting and important results by using this technique. However, the perturbation methods have their own limitations.