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Homotopy perturbation method for bifurcation of nonlinear problems. (English) Zbl 1401.65085
Summary: A simple homotopy is constructed, by the modified Lindstedt-Poincaré method [J.-H. He, Int. J. Non-Linear Mech. 37, No. 2, 309–314 (2002; Zbl 1116.34320)], the solution and the coefficient of linear term are expanded into series of the embedding parameter. Only one iteration leads to accurate solution.

MSC:
65L99 Numerical methods for ordinary differential equations
34E10 Perturbations, asymptotics of solutions to ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
37G10 Bifurcations of singular points in dynamical systems
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