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Application of modified wavelet and homotopy perturbation methods to nonlinear oscillation problems

): x ( t ) = C T ψ ( t ) $$\begin{array}{} \displaystyle x(t) = {C^T}\psi (t) \end{array}$$ (34) Homotopy perturbation method : Solving the nonlinear Eq. (27) using a new approach of homotopy perturbation method, we get x ( t ) = l cos t + sin 2 t 2 2 α l 2 3 + β l 3 4 cos ⁡ t + β l 3 8 cos 2 t + 4 α l 2 3 + β l 3 8 $$\begin{array}{} \displaystyle x(t) = l\,\cos \,t + {\sin ^2}\left( {\frac{t}{2}} \right)\,\left[ {\,\left( {\frac{{2\alpha \,{l^2}}}{3} + \frac{{\beta {l^3}}}{4}} \right)\cos t + \frac{{\beta \,{l^3}}}{8}\cos \,2t + \frac{{4\alpha {l^2}}}{3

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Pierre Liardet (1943–2014)

–27. [L21] G abriel , P.—L emanczyk , M.—L iardet , P.: Ensemble d’invariants pour les produits croisés de Anzai , Mém. Soc. Math. France (N.S.) 47 (1991), 1—102. [L22] K raaikamp , C.–L iardet , P.: Good approximations and continued fractions , Proc. Amer. Math. Soc., 112 (1991), no. 2, 303–309. [L23] B roglio , A.—L iardet , P.: Predictions with automata , in: Symbolic dynamics and its applications (New Haven, CT, 1991), Contemp. Math. Amer. Math. Soc. Vol. 135, Providence, RI, 1992, 111–124. [L24] G oodson , G. R.—K wiatkowski , J.—L emańczyk

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