A modification of the homotopy analysis method based on Chebyshev operational matrices

In this paper a novel approach based on the homotopy analysis method (HAM) is presented for solving nonlinear boundary value problems. This method is based on the operational matrix of Chebyshev polynomials to construct the derivative and product of the unknown function in matrix form. In addition, by using the Tau method the problem is converted to a set of algebraic equations from which the solution can be obtained iteratively. The applicability, accuracy and efficiency of this new Tau modification of the HAM is demonstrated via two examples.