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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. [ABSTRACT FROM AUTHOR]

The paper is devoted to the comparison of different one-dimensional models of blood flow. In such models, the non-Newtonian property of blood is considered. It is demonstrated that for the large arteries, the small parameter is observed in the models, and the perturbation method can be used for the analytical solution. In the paper, the simplified nonlinear problem for the semi-infinite vessel with constant properties is solved analytically, and the solutions for different models are compared. The effects of the flattening of the velocity profile and hematocrit value on the deviation from the Newtonian model are investigated. [ABSTRACT FROM AUTHOR]