On the precise integration methods based on Padé approximations

The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can give precise numerical results approaching exact solutions at the integration points, but it is conditionally stable. By combining Padé approximation and the generalized Padé approximation of...

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Bibliographic Details
Published in:Computers & structures 2009-03, Vol.87 (5), p.380-390
Main Authors: Wang, M.F., Au, F.T.K.
Format: Article
Language:English
Subjects:
Computational techniques
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Generalized Padé approximation
Mathematical methods in physics
Matrix exponential function
Numerical integration
Numerical stability
Physics
Solid mechanics
Structural and continuum mechanics
Structural dynamics
Unconditional stability
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
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Summary:The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can give precise numerical results approaching exact solutions at the integration points, but it is conditionally stable. By combining Padé approximation and the generalized Padé approximation of the matrix exponential function in precise integration, and by using three different types of quadrature formulae, a new generalized family of precise time step integration methods is developed to achieve unconditional stability and arbitrary order of accuracy. Numerical studies indicate that they are unconditionally stable algorithms with controllable numerical dissipation. They also demonstrate the validity and efficiency of these algorithms.
ISSN:0045-7949
1879-2243
DOI:10.1016/j.compstruc.2008.11.004