A Perturbation Method Based on Integrating Factors

DOI10.1137/S0036139996309151zbMath0926.34043MaRDI QIDQ4258460

Wim T. van Horssen

Publication date: 13 September 1999

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

perturbation methodfirst integralsintegrating factorintegrating vectorexact differential equationsasymptotic approximation to first integralexistence and stability of time-periodic solution

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (9)

On constructing solutions for the functional equation \(Z(x, y, n) = Z(a_{11} x + a_{12} y, a_{21} x + a_{22} y, n + 1)\) ⋮ On Invariance Factors and Invariance Vectors for Difference Equations ⋮ On asymptotic approximations of first integrals for second order difference equations ⋮ Exact solutions for certain nonlinear autonomous ordinary differential equations of the second order and families of two-dimensional autonomous systems ⋮ Approximating the amplitude and form of limit cycles in the weakly nonlinear regime of Liénard systems ⋮ On integrating vectors and multiple scales for singularly perturbed ordinary differential equations ⋮ First integrals and analytical solutions of some dynamical systems ⋮ Asymptotic approximations of first integrals for a nonlinear oscillator ⋮ Generalized normal forms for polynomial vector fields

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