A Posteriori Error Estimation and Global Error Control for Ordinary Differential Equations by the Adjoint Method

@article{Cao2004APE,
  title={A Posteriori Error Estimation and Global Error Control for Ordinary Differential Equations by the Adjoint Method},
  author={Yang Cao and Linda R. Petzold},
  journal={SIAM J. Scientific Computing},
  year={2004},
  volume={26},
  pages={359-374}
}
In this paper we propose a general method for a posteriori error estimation in the solution of initial value problems in ordinary differential equations (ODEs). With the help of adjoint sensitivity software, this method can be implemented efficiently. It provides a condition estimate for the ODE system. We also propose an algorithm for global error control, based on the condition of the system and the perturbation due to the numerical approximation. 

Citations

Publications citing this paper.
Showing 1-10 of 29 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 34 references

Estimating the error of numerical solutions of systems of reaction-diffusion equations

  • D. Estep, M. Larson, R. Williams
  • Mem. Amer. Math. Soc., 146
  • 2000
Highly Influential
10 Excerpts

A posteriori error bounds and global error control for approximation of ordinary differential equations

  • D. Estep
  • SIAM J. Numer. Anal., 32
  • 1995
Highly Influential
4 Excerpts

Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations

  • K. E. Brenan, S. L. Campbell, L. R. Petzold
  • Classics Appl. Math. 14, SIAM, Philadelphia
  • 1995
Highly Influential
5 Excerpts

Numerical Initial Value Problems in Ordinary Differential Equations

  • C. W. Gear
  • Prentice– Hall, Englewood Cliffs, NJ
  • 1971
Highly Influential
4 Excerpts

Similar Papers

Loading similar papers…