In the framework of the Homotopy Analysis Method (HAM) the so-called convergence-control parameter c0 (Liao (Int J Non-Linear Mech 32:815–822, 1997) originally used the symbol to denote the auxiliary parameter. But, is well-known as Planck’s constant in quantum mechanics. To avoid misunderstanding, Liao (Commun Nonlinear Sci Numer Simulat 15:2003–2016, 2010) suggest to use the symbol c0 to denote the basic convergence-control parameter.) has a key role in convergence of obtained series solution of solving non-linear equations. In this paper a modified approach in the determining of the convergence-control parameter value c0 is proposed. The purpose of this paper is to find a proper convergence-control parameter c0 to get a convergent series solution, or a faster convergent one. This modified approach minimizes the norm of a discrete residual function, systematically, in which seeks to find an optimal value of the convergence-control parameter c0 at each order of HAM approximation, instead of the so-called c0-curve process. The proved theorems and numerical results demonstrate the validity, efficiency, and performance of the proposed approach.
کلید واژگان :Two-point boundary value problem · Homotopy Analysis Method · Optimal value · Convergence-control parameter
ارزش ریالی : 1200000 ریال
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