Acta Mechanica Solida Sinica

, Volume 19, Issue 4, pp 289–296 | Cite as

A predict-correct numerical integration scheme for solving nonlinear dynamic equations

  • Jianping Fan
  • Tao Huang
  • Chak-yin Tang
  • Cheng Wang


A new numerical integration scheme incorporating a predict-correct algorithm for solving the nonlinear dynamic systems was proposed in this paper. A nonlinear dynamic system governed by the equation = F (v, t) was transformed into the form as = Hv + f (v, t). The nonlinear part f (v, t) was then expanded by Taylor series and only the first-order term retained in the polynomial. Utilizing the theory of linear differential equation and the precise time-integration method, an exact solution for linearizing equation was obtained. In order to find the solution of the original system, a third-order interpolation polynomial of v was used and an equivalent nonlinear ordinary differential equation was regenerated. With a predicted solution as an initial value and an iteration scheme, a corrected result was achieved. Since the error caused by linearization could be eliminated in the correction process, the accuracy of calculation was improved greatly. Three engineering scenarios were used to assess the accuracy and reliability of the proposed method and the results were satisfactory.

Key words

nonlinear dynamics direct integration method internal resonance saturation phenomenon jumping phenomenon bifurcation 


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2006

Authors and Affiliations

  • Jianping Fan
    • 1
  • Tao Huang
    • 1
  • Chak-yin Tang
    • 2
  • Cheng Wang
    • 1
  1. 1.Institute of Engineering Calculation & SimulationHuazhong University of Science & TechnologyWuhanChina
  2. 2.Department of Industrial and Systems EngineeringThe Hong Kong Polytechnic UniversityHong KongChina

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