Homotopy perturbations method: Theoretical as­pects and applications

Integral Transforms with the Homotopy Perturbation Method and Some Applications

Approximation theory covers some important topics in applied analysis, and its application serves many fields in science and engineering such as fluid mechanics, electromagnetism, diffraction theory, statistics and economics. Although it is an old subject, dating back to Laplace, new methods and applications continue to appear in various publications. There is now a need to provide new methods ...

The comparison of optimal homotopy asymptotic method and homotopy perturbation method to solve Fisher equation

In recent years, numerous approaches have been applied for finding the solutions of functional equations. One of them is the optimal homotopy asymptotic method. In current paper, this method has been applied for obtaining the approximate solution of Fisher equation. The reliability of the method will be shown by solving some examples of various kinds and comparing the obtained outcomes with the ...

Applications of the homotopy analysis method to optimal control problems

Singh, Shubham, MS, Purdue University, August 2016. Applications of the Homotopy Analysis Method to Optimal Control Problems. Major Professor: Michael J. Grant. Traditionally, trajectory optimization for aerospace applications has been performed using either direct or indirect methods. Indirect methods produce highly accurate solutions but suffer from a small convergence region, requiring initi...

Applications of Homotopy Perturbation Method for Nonlinear Partial Differential Equations

The Drinfeld-Sokolov (DS) system was first introduced by Drinfeld and Sokolov and it is a system of nonlinear partial differential equations owner of the Lax pairs of a special form [1]. The physical motivation of this system was explained in detail by Ref.[2]. Generalized form of the DS system has been studied by different authors using the various methods [3, 4, 5, 6, 7, 8, 9, 10]. In order t...

Categorical aspects of equivariant homotopy