New Approach of Homotopy Perturbation Method for Solving the Equations in Enzyme Biochemical Systems

Kurunatha Perumal Thevar Vijayan Preethi

doi:10.11648/j.acm.20170603.14

Abstract

In this paper, new homotopy perturbation method (iteration scheme) will be employed to solve the nonlinear dynamical problems that arise in thin membrane kinetics. More precisely, the method will be used to mathematically model and solve the kinetics of the thin membrane. A main property that makes the proposed method superior to other iterative methods is the way it handles boundary value problems, where both mixed Dirichlet and Neumann boundary conditions are taken into consideration, while other iterative methods only make account of the initial point and as a result, the approximate solution may deteriorate for values that are far away from the initial point and closer to the other endpoint. Our analytical results are compared with numerical solution. The method is found to be easily implemented, fast, and computationally economical and attractive.

Highlights

Non-linear differential equations can model many phenomena in different fields of science and engineering in order to present their behaviors and effects by mathematical concepts
The homotopy perturbation method is used by Nourazar et al [4,5,6] in order to obtain exact solution of nonlinear differential equations
In this study we have applied NHPM to find the approximate solution of the problem of the second order non-linear differential equation in thin membrane

Summary

Introduction

Non-linear differential equations can model many phenomena in different fields of science and engineering in order to present their behaviors and effects by mathematical concepts. In order to obtain exact solution of nonlinear differential equations, semi-analytical methods such as the Variational Iteration method (VIM) and Homotopy perturbation method (HPM) are considered. The ideas of the VIM and HPM were first pioneered by He [1, 2] He [3] presented application of the HPM in solving the nonlinear non-homogeneous partial differential equations. In this study we have applied NHPM to find the approximate solution of the problem of the second order non-linear differential equation in thin membrane. This method generate the analytical solutions in convergence series and it is effective mathematical tool to handle a large class of linear and non-. Kurunatha Perumal Thevar Vijayan Preethi et al.: New Approach of Homotopy Perturbation Method for Solving the Equations in Enzyme Biochemical Systems linear differential equation in engineering and chemical sciences

Mathematical Formulation of the Problem

Solution of Boundary Value Problem Using HPM

Numerical Simulation

Discussions

Conclusion