The Least Squares Homotopy Perturbation Method for Systems of Differential Equations with Application to a Blood Flow Model

Abstract

In this paper, least squares homotopy perturbation is presented as a straightforward and accurate method to compute approximate analytical solutions for systems of ordinary differential equations. The method is employed to solve a problem related to a laminar flow of a viscous fluid in a semi-porous channel, which may be used to model the blood flow through a blood vessel, taking into account the effects of a magnetic field. The numerical computations show that the method is both easy to use and very accurate compared to the other methods previously used to solve the given problem.

Keywords

• least squares homotopy perturbation method
• system of nonlinear differential equations
• approximate analytical solutions
• non-Newtonian fluid
• magnetohydrodynamics