论文信息 - A Simple Approach of Enlarging Convergence Regions of Perturbation Approximations

A Simple Approach of Enlarging Convergence Regions of Perturbation Approximations

In this paper, a simple approach to enlarging convergence regions of perturbation approximations is proposed. Based on the so-called general Taylor theorems, this approach has a solid mathematical foundation. Moreover, it is rather simple to apply. Two nonlinear equations, the Riccati equation and the Van der Pol equation are used as examples to illustrate the validity and the great potential of this approach.

S. Liao | Shi-Jun Liao

[1] James F. Geer,et al. Perturbation analysis of the limit cycle of the free van der Pol equation , 1984 .

[2] James F. Geer,et al. Power Series Expansions for the Frequency and Period of the Limit Cycle of the Van Der Pol Equation , 1982 .

[3] Shijun Liao,et al. AN APPROXIMATE SOLUTION TECHNIQUE WHICH DOES NOT DEPEND UPON SMALL PARAMETERS (PART 2): AN APPLICATION IN FLUID MECHANICS , 1997 .

[4] Solutions to Van der Pol's equation using a perturbation method , 1967 .

[5] Shaohua Chen,et al. On perturbation procedure for limit cycle analysis , 1991 .

[6] S. Liao. On the general boundary element method , 1998 .

[7] Shijun Liao,et al. AN APPROXIMATE SOLUTION TECHNIQUE WHICH DOES NOT DEPEND UPON SMALL PARAMETERS: A SPECIAL EXAMPLE , 1995 .

[8] Vimal Singh,et al. Perturbation methods , 1991 .

[9] S. Liao. An explicit, totally analytic approximate solution for Blasius’ viscous flow problems , 1999 .

[10] J. Grasman,et al. The method of matched asymptotic expansions for the periodic solution of the van der pol equation , 1973 .

[11] S. Liao. A kind of approximate solution technique which does not depend upon small parameters — II. An application in fluid mechanics , 1997 .

[12] S. Liao. A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate , 1999, Journal of Fluid Mechanics.

[13] A. Nayfeh. Introduction To Perturbation Techniques , 1981 .