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Supervised by Ministry of Industry and Information Technology of The People's Republic of China Sponsored by Harbin Institute of Technology Editor-in-chief Yu Zhou ISSNISSN 1005-9113 CNCN 23-1378/T

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Related citation:Chen Chen,Pingkang Li.A Recursive Algorithm for Nonlinear Dynamical System Analysis Based on ADM[J].Journal of Harbin Institute Of Technology(New Series),2016,23(1):46-52.DOI:10.11916/j.issn.1005-9113.2016.01.007.
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A Recursive Algorithm for Nonlinear Dynamical System Analysis Based on ADM
Author NameAffiliation
Chen Chen School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China 
Pingkang Li School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China 
Abstract:
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.
Key words:  adomian decomposition method  nonlinear dynamical system  analytic solution  truncation order
DOI：10.11916/j.issn.1005-9113.2016.01.007
Clc Number:O175.1
Fund:

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