Maintaining the stability of nonlinear differential equations by the enhancement of HPM. (English) Zbl 1220.70018

Summary: Homotopy perturbation method is an effective method to find a solution of a nonlinear differential equation. In this method, a nonlinear complex differential equation is transformed to a series of linear and nonlinear parts, almost simpler differential equations. These sets of equations are then solved iteratively. Finally, a linear series of the solutions completes the answer if the convergence is maintained. In this Letter, the need for stability verification is shown through some examples. Consequently, HPM is enhanced by a preliminary assumption. The idea is to keep the inherent stability of nonlinear dynamic, even the selected linear part is not.


70K20 Stability for nonlinear problems in mechanics
70H09 Perturbation theories for problems in Hamiltonian and Lagrangian mechanics
34A34 Nonlinear ordinary differential equations and systems
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