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Zbl 1222.65090
Motsa, S.S.; Sibanda, P.; Shateyi, S.
A new spectral-homotopy analysis method for solving a nonlinear second order BVP. (English)
[J] Commun. Nonlinear Sci. Numer. Simul. 15, No. 9, 2293-2302 (2010). ISSN 1007-5704

Summary: A modification of the homotopy analysis method (HAM) for solving nonlinear second-order boundary value problems (BVPs) is proposed. The implementation of the new approach is demonstrated by solving the Darcy--Brinkman--Forchheimer equation for steady fully developed fluid flow in a horizontal channel filled with a porous medium. The model equation is solved concurrently using the standard HAM approach and numerically using a shooting method based on the fourth order Runge--Kutta scheme. The results demonstrate that the new spectral homotopy analysis method is more efficient and converges faster than the standard homotopy analysis method.

MSC 2000:: *65L99 Numerical methods for ODE

Keywords: homotopy analysis method; Chebyshev spectral method; brinkman; Forchheimer model

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Zentralblatt MATH Berlin [Germany]