Abstract
We present a new modification of the homotopy perturbation method (HPM) for solving nonlinear boundary value problems. The technique is based on the standard homotopy perturbation method, and blending of the Chebyshev pseudospectral methods. The implementation of the new approach is demonstrated by solving the Jeffery-Hamel flow considering the effects of magnetic field and nanoparticle. Comparisons are made between the proposed technique, the standard homotopy perturbation method, and the numerical solutions to demonstrate the applicability, validity, and high accuracy of the present approach. The results demonstrate that the new modification is more efficient and converges faster than the standard homotopy perturbation method.
Highlights
Many problems in the fields of physics, engineering, and biology are modeled by coupled linear or nonlinear systems of partial or ordinary differential equations
In generating the presented results, it was determined through numerical experimentation that N = 80 and we considered the fourth-order of spectral-homotopy perturbation method (SHPM) which gave sufficient accuracy for the method
We have proposed a modification of the standard homotopy perturbation method for solving nonlinear ordinary differential equations
Summary
Many problems in the fields of physics, engineering, and biology are modeled by coupled linear or nonlinear systems of partial or ordinary differential equations. One of these methods is the homotopy perturbation method (HPM) This method, which is a combination of homotopy in topology and classic perturbation techniques, provides us with a convenient way to obtain analytic or approximate solutions for a wide variety of problems arising in different scientific fields by continuously deforming the difficult problem into a set of simple linear problems that are easy to solve. It was proposed first by He [1,2,3,4]. The obtained results give rapid convergence, good accuracy and suggest that this newly improvement technique introduces power for solving nonlinear boundary value problems and several advantages of the SHPM over the HPM approach are pointed out
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