Modified Lindstedt–Poincare methods for some strongly non-linear oscillations: Part II: a new transformation

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Nonlinear oscillator with discontinuity by parameter-expansion method (2008, unknown): “The parameter-expansion method [18–21] entails the bookkeeping parameter method [18,19] and the modified Lindstedt–Poincare method [18,21–23].”
Application of Parameter-expanding Method to Strongly Nonlinear Oscillators (2007, unknown): “Parameter-expanding Method Recently parameter-expanding methods [18,20,21] including bookkeeping parameter method[19] and modified Lindstedt-Poincare methods[22-25] have been caught much attention, the parameter expansion can also be applied to homotopy perturbation method[26].”
Homotopy Perturbation Method for Bifurcation of Nonlinear Problems (2005, background): “(12) 1 4 The solution of (11), considering the boundary conditions w, (0) = μ, (π) = 0 , and the additional condition μ, (λγ/2) = 0 , is”
A NEW PERTURBATION ALGORITHM WITH BETTER CONVERGENCE PROPERTIES: MULTIPLE SCALES LINDSTEDT POINCARE METHOD (2009, methodology): “Among the many developed methods, Linearized perturbation method [4-6], parameter expanding method [7, 8], new time transformations as modifications of Lindstedt-Poincare method [9-11], iteration methods [12, 13] are some examples.”