... of the problem. Design/methodology/approach This study combines Sawi transform (ST) and the homotopy perturbation method (HPM) to formulate the idea of Sawi homotopy perturbation transform method (SHPTM). First, this study implements ST to handle the recurrence relation and then incorporates HPM to derive...

... and homotopy perturbation method (HPM), is used to elaborate the analytical solution of this system. The main focus of He-Laplace method is to find the Lagrange multiplier with an easy approach which enables the implementation of HPM very smoothly and provides the series solution very close to the exact...

.... In this part, the authors apply the fractional complex transform (the two-scale transform) to convert the problem into its differential partner, and then they introduce the homotopy perturbation method (HPM) to bring down the nonlinear terms for the approximate solution. Findings The HPM makes numerical...

... only Homotopy perturbation method Fractional differential equation Mohand transform Newell–Whitehead–Segel equation Approximate solution Fractional NWSE In daily life, many physical systems are usually demonstrated in various extended areas such that uniform, oscillatory and chaotic...

... derivatives are defined to construct a novel approach. Second, modified Laplace homotopy perturbation method (HPM) is constructed which yields to a direct approach. Third, two numerical examples are presented to show the accuracy of this derived method and graphically results showed that this method is very...

... analytical solution is found by using two-scale method and homotopy perturbation method (HPM). Design/methodology/approach The author establishes a new fractal model based on He’s fractal derivative in a microgravity space and its variational principle is obtained via the semi-inverse method...

... Fractional calculus Laplace transform Homotopy perturbation method Fractional calculus usually solved numerous physical and engineering phenomena defining fractional partial differential equations (FPDEs). The concept of fractional calculus was introduced in the 19th century by Riemann...

... calculus have been introduced. Some analytical methods are reviewed, mainly including the variational iteration method, the Ritz method, the homotopy perturbation method, the variational principle and the Taylor series method. An example is given to show the simple solution process and the high accuracy...

.... As such, we have applied Galerkin’s method and homotopy perturbation method (HPM) to study the natural convection of non-Newtonian nanofluid and the real fluid flow between two vertical parallel plates also that of real fluid. This paper aims to investigate the natural convection of non-Newtonian...

... 07 05 2017 © Emerald Publishing Limited 2018 Emerald Publishing Limited Licensed re-use rights only Homotopy perturbation method Symmetry Boundary value problem Differential characteristic set algorithm Runge–Kutta method The symmetry method, originally developed...

...Perumandla Karunakar; Snehashish Chakraverty Purpose This paper aims to solve linear and non-linear shallow water wave equations using homotopy perturbation method (HPM). HPM is a straightforward method to handle linear and non-linear differential equations. As such here, one-dimensional shallow...

... perturbation methods (LTHPM) are considered as an algorithm which converges rapidly to the exact solution of the nonlinear Boussinesq equation. Design/methodology/approach – The authors present the solution of nonlinear Boussinesq equation by combination of Laplace transform and new homotopy perturbation...

...Yanqin Liu; Lihua Dong Purpose – The purpose of this paper is to apply a new modified homotopy perturbation method, which is effective to solve multi-order fractional equations with non-polynomial initial and boundary conditions. Design/methodology/approach – The proposed algorithm...

...Dr Hong-Yan Liu and Dr Ji-Huan He; Guanglu Zhou; Boying Wu Purpose – The purpose of this paper is to present a general framework of Homotopy perturbation method (HPM) for analytic inverse heat source problems. Design/methodology/approach – The proposed numerical technique is based on HPM...

... al., 2011) and fractional homotopy perturbation method (HPM) (Khan et al., 2012) so on. For any positive integer k and α, the following equality holds: Equation 5 where f(αk)(x) is the derivative of order αk of continuous function f(x...

...S. Karimi Vanani; A. Yildirim; F. Soleymani; M. Khan; S. Tutkun Purpose The purpose of this paper is to present a weighted algorithm based on the homotopy perturbation method for solving the heat transfer equation in the cast‐mould heterogeneous domain. Design/methodology/approach A weighted...

...Jafar Biazar; Mostafa Eslami Purpose The purpose of this study is to propose an analytical approach based on the homotopy perturbation method (HPM) for solving the initial value problems associated with the Fornberg‐Whitham type equations. Design/methodology/approach In this paper, He's HPM...

...Mehdi Dehghan; Jalil Manafian Heris Purpose This paper aims to show that the variational iteration method (VIM) and the homotopy perturbation method (HPM) are powerful and suitable methods to solve the Fornberg‐Whitham equation. Design/methodology/approach Using HPM the explicit exact solution...

...Ahmet Yıldırım; Hüseyin Koçak Purpose The purpose of this paper is to implement the variational iteration method and the homotopy perturbation method to give a rational approximation solution of the foam drainage equation with time‐ and space‐fractional derivatives. Design/methodology/approach...

...Syed Mohyud‐Din; Ahmet Yıldırım; Yagmur Gulkanat Purpose The aim of this paper is to present the numerical simulation of the population dynamics model with density‐dependent migrations and the Allee effects using the homotopy perturbation method (HPM). Design/methodology/approach The paper...