Structural Engineering and Mechanics

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On a new fourth order self-adaptive time integration algorithm

  • Zhong, Wanxie (Research Institute of Engineering Mechanics, Dalian University of Technology) ;
  • Zhu, Jianping (Department of Mathematics and Statistics, Mississippi State University)
  • Published : 1996.11.25
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Abstract

An explicit 4th order time integration scheme for solving the convection-diffusion equation is discussed in this paper. A system of ordinary differential equations are derived first by discretizing the spatial derivatives of the relevant PDE using the finite difference method. The integration of the ODEs is then carried out using a 4th order scheme and a self-adaptive technique based on the spatial grid spacing. For a non-uniform spatial grid, different time step sizes are used for the integration of the ODEs defined at different spatial points, which improves the computational efficiency significantly. A numerical example is also discussed in the paper to demonstrate the implementation and effectiveness of the method.

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References

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Cited by

  1. Extended implicit integration process by utilizing nonlinear dynamics in finite element vol.64, pp.4, 1996, https://doi.org/10.12989/sem.2017.64.4.495