Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM) for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF) and numerical solu...

In this continuation of a series of our earlier papers, we define a hypersurface h(x, t) = 0 in terms of the unknown vector x, and a monotonically increasing function Q(t) of a time-like variable t, to solve a system of nonlinear algebraic equations F(x) = 0. If R is a vector related to ∂h/∂x, we consider the evolution equation ẋ = λ [αR+βP], where P = F−R(F ·R)/‖R‖2 such that P ·R = 0; or ẋ = ...