Mathematical properties of h-curve in the frame work of the homotopy analysis method
Abbreviated Journal Title
Commun. Nonlinear Sci. Numer. Simul.
Homotopy analysis method; Convergence-controller parameter; h-curve; Horizontal line; BOUNDARY-LAYER-FLOW; ANALYTIC SOLUTION; STRETCHING SHEET; HEAT-TRANSFER; AXISYMMETRICAL FLOW; EXPLICIT SOLUTION; 3RD-GRADE FLUID; 3RD-ORDER; FLUID; KDV EQUATION; SOLVE; Mathematics, Applied; Mathematics, Interdisciplinary Applications; Mechanics; Physics, Fluids & Plasmas; Physics, Mathematical
As it is described in the frame work of the homotopy analysis method (HAM), the convergence-control parameter is the main auxiliary tool which distinguishes this method form the other analytical methods. Moreover the convergence is usually obtained by the so-called h-curve which possesses horizontal line property. The purpose of this paper is to answer this fundamental question: That is, why the horizontal line occurs in the plot of HAM series solution at some points corresponding to the convergence-control parameter. Also, the mathematical proof and the properties of this main issue are presented. Furthermore, some illustrative examples are presented and the salient features are discussed. (C) 2011 Elsevier B.V. All rights reserved.
Communications in Nonlinear Science and Numerical Simulation
"Mathematical properties of h-curve in the frame work of the homotopy analysis method" (2011). Faculty Bibliography 2010s. 1027.