Application of variational iteration method to nonlinear heat transfer equations using He's polynomials

Abstract

Purpose -The purpose of this paper is to solve an unsteady nonlinear convective-radiative equation and a nonlinear convective-radiative-conduction equation containing two small parameters of 1 1 and 1 2 by variational homotopy perturbation method. Design/methodology/approach -The heat transfer equations are described. The variational homotopy perturbation method as a powerful method for solving linear and nonlinear equations is applied to find the solutions of our model equations.Findings -The solutions of heat transfer equations are calculated in the form of convergent series with easily computable components. Two examples are solved as illustrations, using symbolic computation. Originality/value -The results show that the suggested method is easy to implement and has high level of accuracy. The method introduces a reliable tool for solving many linear and nonlinear differential equations. Nomenclature

The variational homotopy perturbation method for solving the K(2,2)equations

“…To illustrate the concept of the variational homotopy perturbation method [14] [matinfar2] we consider the general differential equation (5). We construct the correction functional (6) and apply the homotopy perturbation method to obtain [12,14].…”

“…We construct the correction functional (6) and apply the homotopy perturbation method to obtain [12,14].…”

New iterative method for solving gas dynamic equation

“…Therefore, from (2.5), we can obtain easily the following .first few components of the new iterative solution for the equation (3.1): , which is the same result obtained by HPM [14], LTNHPM [15], and VIMHP [16]. which will reduce to the following form:…”

“…which is the exact solution by one step .The other methods, LTNHPM [15], and VIMHP [16], take more than one step to reached the exact or approximation solution. This problem is solved in [15], by LTNHPM, the six term approximate solution takes the form: From comparison, it is clear that the rate of convergence of NIM is faster than, LTNHPM, VIMHP.…”

Elzaki Transform Homotopy Perturbation Method for Solving Gas Dynamics Equation

“…This is the solution of (21) and which is exactly the exact solution of the problem [2,3,4,5]. Figure 2 …”