摘要
To improve the limitation of Adomian finite term series solution reducing the convergence for nonlinear dynamical systems, a recursive algorithm for nonlinear systems analysis based on Adomian Decomposition Method( ADM) with suitable truncation order is proposed. The recursive algorithm makes use of Differential Transformation( DT) theory to convert the analytic solution from series into matrix,and then the solution matrix is used in each discrete interval to compute numerical solution iteratively. The maximum stable step-size criterion using recursion percent error( RPE) is developed for good convergence in each iteration. As classic nonlinear dynamical equations,the second-order equation with one RPE and the coupling Duffing equations with two RPEs are illustrated. Comparison results demonstrate that the presented algorithm is valid and applicable to nonlinear dynamical systems analysis.
To improve the limitation of Adomian finite term series solution reducing the convergence for nonlinear dynamical systems, a recursive algorithm for nonlinear systems analysis based on Adomian Decomposition Method（ ADM） with suitable truncation order is proposed. The recursive algorithm makes use of Differential Transformation（ DT） theory to convert the analytic solution from series into matrix,and then the solution matrix is used in each discrete interval to compute numerical solution iteratively. The maximum stable step-size criterion using recursion percent error（ RPE） is developed for good convergence in each iteration. As classic nonlinear dynamical equations,the second-order equation with one RPE and the coupling Duffing equations with two RPEs are illustrated. Comparison results demonstrate that the presented algorithm is valid and applicable to nonlinear dynamical systems analysis.
基金
Sponsored by the National Natural Science Foundation of China(Grant No.61074104)
