In this paper, we suggest and analyze some iterative methods for solving nonlinear equations using the homotopy perturbation technique coupled with system of equations. In addition, we show that the homotopy polynomial is exactly the the Adomian polynomial and this establishes the equivalence between the homotopy perturbation and decomposition techniques. Our method of establishing the equivale...

In this paper, the homotopy perturbation method (HPM) is applied to obtain an approximate solution of the fractional Bratu-type equations. The convergence of the method is also studied. The fractional derivatives are described in the modied Riemann-Liouville sense. The results show that the proposed method is very ecient and convenient and can readily be applied to a large class of fractional p...

Aim of the paper is to investigate applications of Homotopy Perturbation Method(HPM) on non-linear physical problems .Some coupled non-linear partial differential equations are considered and solved numerically using Homotopy Perturbation Method. The results obtained by HPM are compared with those obtained by Adomian Decomposition Method. The behavior of Homotopic solution is shown through grap...

In this paper, we study semi-analytical methods entitled Homotopy pertourbation method (HPM) to solve fuzzy impulsive fractional differential equations based on the concept of generalized Hukuhara differentiability. At the end first of Homotopy pertourbation method is defined and its properties are considered completely. Then econvergence theorem for the solution are proved and we will show tha...

A new treatment for homotopy perturbation method is introduced. The new treatment is called He-Laplacemethodwhich is the coupling of the Laplace transform and the homotopy perturbation method using He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The method is implemented on linear and nonlinear partial differential equations. It is found that the prop...

Laplace transform and new homotopy perturbation methods are adopted to study Fisher-type equations analytically. The solutions introduced in this study can be used to obtain the closed form of the solutions if they are required. The combined method needs less work in comparison with the other homotopy perturbation methods and decreases volume of calculations considerably. The method is tested o...

In this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the Maclaurin series of the exact solution. Nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. These equations equip a significant mathematical model for dynamical systems. The accuracy o...

In this paper, the piecewise homotopy perturbation method (PHPM) is employed to solve the Hamilton– Jacobi–Bellman (HJB) equation arising in the optimal control problems. The method is a simple modification of the standard homotopy perturbation method (HPM), in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the...

More recently, Wazwaz [An analytic study of Fisher’s equation by using Adomian decomposition method, Appl. Math. Comput. 154 (2004) 609–620] employed the Adomian decomposition method (ADM) to obtain exact solutions to Fisher’s equation and to a nonlinear diffusion equation of the Fisher type. In this paper, He’s homotopy perturbation method is employed for the generalized Fisher’s equation to o...

Inthispaper,wesolveHamilton-Jocobi-Bellman(HJB)equationsarisinginoptimalcontrolproblems usingHomotopyPerturbationTransformMethod(HPTM).Theproposedmethodisacombinedform oftheLaplaceTransformationMethodwiththeHomotopyPerturbationMethodtoproduceahighly effectivemethodtohandlemanyproblems. ApplyingtheHPTM,solutionprocedurebecomeseasier, simplerandmorestraightforward. Someillustrativeexamplesaregive...