摘要
The KBM method is effective in solving nonlinear problems.Unfortunately,the traditional KBM method strongly depends on a small parameter,which does not exist in most of the practice physical systems.Therefore this method is limited to dealing with the system with strong nonlinearity.In this paper we present a procedure to study the resonance solutions of the system with strong nonlinearities by employing the homotopy analysis technique to extend the KBM method to the strong nonlinear systems,and we also analyze the truncation error of the procedure.Applied to a given example,the procedure shows the efficiencies in studying bifurcation.
The KBM method is effective in solving nonlinear problems.Unfortunately,the traditional KBM method strongly depends on a small parameter,which does not exist in most of the practice physical systems.Therefore this method is limited to dealing with the system with strong nonlinearity.In this paper we present a procedure to study the resonance solutions of the system with strong nonlinearities by employing the homotopy analysis technique to extend the KBM method to the strong nonlinear systems,and we also analyze the truncation error of the procedure.Applied to a given example,the procedure shows the efficiencies in studying bifurcation.
基金
supported by the National Natural Science Foundation of China (Grant No.10632040)
