A NEW APPROACH TO DETERMINE THE CONVERGENCE-CONTROL PARAMETER IN THE APPLICATION OF THE HOMOTOPY ANALYSIS METHOD TO SYSTEMS OF LINEAR EQUATIONS

作者：Ghanbari M^*; Abba**andy S; Allahviranloo T

来源：Applied and Computational Mathematics, 2013, 12(3): 355-364.

• Homotopy Analysis Method
• Homotopy Perturbation Method
• System of Linear Equations
• Convergence-Control Parameter

It is well known that the application of the homotopy analysis method (HAM) to various problems can determine the valid region of the convergence-control parameter h, either by plotting the so-called h-curve, or by minimizing the residual error. In this paper, we present a new approach based on the spectral radius of the coefficient matrix to obtain a proper value of h, when the HAM is applied to systems of linear equations. We also present a detailed discussion about the convergence of the HAM, and give a necessary and sufficient condition for the obtained results, when the HAM is used for solving a system of linear equations.

• 出版日期2013