Citation: | HE Ji-huan. A Note on Delta-Perturbation Expansion Method[J]. Applied Mathematics and Mechanics, 2002, 23(6): 558-562. |
[1] |
Bender C M, Pinsky K S, Simmons L M. A new perturbative approach to nonlinear problems[J]. J Math Phys,1989,30(7):1447-1455.
|
[2] |
Awrejcewicz J, Andrianov I V, Manevitch L I. Asymptotic Approaches in Nonlinear Dynamics: New Trends and Applications[M]. Heidelberg: Springer,1998.
|
[3] |
HE Ji-huan. Homotopy perturbation technique[J]. Computer Methods in Applied Mechanics and Engineering,1999,178(3/4):257-262.
|
[4] |
HE Ji-huan. A coupling method of homotopy technique and perturbation technique for nonlinear problems[J]. Int J Nonl Mech,2000,35(1):37-43.
|
[5] |
HE Ji-huan. A new perturbation technique which is also valid for large parameters[J]. Journal of Sound and Vibration,2000,229(5):1257-1263.
|
[6] |
HE Ji-huan. A review on some new recently developed nonlinear analytical techniques[J]. International Journal of Nonlinear Sciences and Numerical Simulation,2000,1(1):51-70.
|
[7] |
Andrianov I, Awrejcewicz J. Construction of periodic solution to partial differential equations with nonlinear boundary conditions[J]. International Journal of Nonlinear Sciences and Numerical Simulation,2000,1(4):327-332.
|
[8] |
HE Ji-huan. Iteration perturbation method for strongly nonlinear oscillations[J]. Journal of Vibration and Control,2001,7(5):631-642.
|
[9] |
Acton J R, Squire P T. Solving Equations With Physical Understanding[M]. Bristol and Boston: Adam Hilger Ltd,1985.
|
[10] |
HE Ji-huan. Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations Part Ⅰ: expansion of a constant[J]. International Journal of Non-Linear Mechanics,2002,37(2):309-314.
|
[11] |
HE Ji-huan. Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations Part Ⅱ: a new transformation[J]. International Journal of Non-Linear Mechanics,2002,37(2):315-320.
|
[12] |
HE Ji-huan. Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations Part Ⅲ: double series expansion[J]. International Journal of Non-Linear Science and Numerical Simulation,2001,2(4):317-320.
|
[13] |
HE Hi-huan. Bookkeeping parameter in perturbation methods[J]. International Journal of Non-Linear Science and Numerical Simulation,2001,2(3):257-264.
|
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[15] | Liao Shijun, . Homotopy Analysis Method: a New Analytic Method for Nonlinear Problems[J]. Applied Mathematics and Mechanics, 1998, 19(10): 885-890. |
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[17] | Jiang Xiaoyu, Zhang Xiangzhou, Chen Baipin. Nonlinear Three-Dimensional Analysis of Composite Laminated Plates[J]. Applied Mathematics and Mechanics, 1996, 17(7): 589-600. |
[18] | Zhu Yong. Head-on Collision between Two mKdV Solitary Waves in a Two-Layer Fluid System[J]. Applied Mathematics and Mechanics, 1992, 13(5): 389-399. |
[19] | Yue Xiang-an, Kong Xiang-yan, Chen Jia-lang. Perturbation Solution of Non-Newtonian Fluid Axial Laminar Flow through Eccentric Annuli[J]. Applied Mathematics and Mechanics, 1992, 13(3): 245-254. |
[20] | Zhang Rong-xiang, Chen Zhao-kuan. Application of the Theory of Branching of Solutions of Nonlinear Equations to the Estimation of Pole Perturbance of Linear Closed-Loop Systems[J]. Applied Mathematics and Mechanics, 1982, 3(5): 661-670. |