Solutions to Van der Pol's equation using a perturbation method
作者： R.T. Davis , K.T. Alfriend
DOI: 10.1016/0020-7462(67)90011-X
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摘要: Abstract Solutions to Van der Pol's equation are examined when the coefficient e of non-linear term is small. Under this condition a uniformly valid second approximation for arbitrary initial conditions obtained using perturbation method first developed by Cochran and extended Nayfeh. The work here then obtain fourth time variations in limit cycle. Comparison made between solutions those numerical integration.
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MINORU URABE, Numerical Study of Periodic Solutions of the van der Pol Equation International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics. pp. 184- 192 ,(1963) , 10.1016/B978-0-12-395651-4.50024-6
G.F. Carrier, Boundary Layer Problems in Applied Mechanics Advances in Applied Mechanics. ,vol. 3, pp. 1- 19 ,(1953) , 10.1016/S0065-2156(08)70206-0
Nikolai Mitrofanovich Krylov, Nikolai Nikolaevich Bogoliubov, None, Introduction to non-linear mechanics Princeton university press , H. Milford, Oxford university press. ,(1943)
Ali Hasan Nayfeh, An Expansion Method for Treating Singular Perturbation Problems Journal of Mathematical Physics. ,vol. 6, pp. 1946- 1951 ,(1965) , 10.1063/1.1704745