The arbitrary order implicit multistep schemes of exponential fitting and their applications

  • Authors:

  • Chen Tang;Haiqing Yan;Hao Zhang;Zhanqing Chen;Ming Liu;Guimin Zhang

  • Affiliations:

  • Department of Applied Physics, University of Tianjin, Tianjin 300072, PR China;Department of Applied Physics, University of Tianjin, Tianjin 300072, PR China;Department of Applied Physics, University of Tianjin, Tianjin 300072, PR China;Department of Mechanical Engineering and Automation, Harbin Institute of Technology, Harbin, PR China;Department of Applied Physics, University of Tianjin, Tianjin 300072, PR China;Department of Applied Physics, University of Tianjin, Tianjin 300072, PR China

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2005

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Abstract

We develop the arbitrary order implicit multistep schemes of exponential fitting (EF) for systems of ordinary differential equations. We use an explicit EF scheme to predict an approximation, and then use an implicit EF scheme to correct this prediction. This combination is called a predictor-corrector EF method. We demonstrate the accuracy and efficiency of the new predictor-corrector methods via application to a variety of test cases and comparison with other analytical and numerical results. The numerical results show that the schemes are highly accurate and computationally efficient.