Skip to main content
Log in

Numerical fixed grid methods for differential inclusions

  • Published:
Computing Aims and scope Submit manuscript

Summary

Numerical methods for initial value problems for differential inclusions usually require a discretization of time as well as of the set valued right hand side. In this paper, two numerical fixed grid methods for the approximation of the full solution set are proposed and analyzed. Convergence results are proved which show the combined influence of time and (phase) space discretization.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aubin J.P. and Cellina A. (1984). Differential inclusions. Grundlehren der mathematischen Wissenschaften, vol. 264. Springer, Berlin

    Google Scholar 

  • Chahma I.A. (2003). Set-valued discrete approximation of state-constrained differential inclusions. Bayreuth Math Schr 67: 3–161

    MathSciNet  Google Scholar 

  • Dontchev A. and Farkhi E. (1988). Error estimates for discretized differential inclusions. Computing 41: 349–358

    Article  MathSciNet  Google Scholar 

  • Dontchev A. and Lempio F. (1992). Difference methods for differential inclusions: a survey. SIAM Rev 34(2): 263–294

    Article  MATH  MathSciNet  Google Scholar 

  • Grammel G. (2003). Towards fully discretized differential inclusions. Set-Valued Anal 11: 1–8

    Article  MATH  MathSciNet  Google Scholar 

  • Grüne L. (2002). Asymptotic behavior of dynamical systems and control systems under perturbation and discretization. Springer, Heidelberg

    MATH  Google Scholar 

  • Grüne L. and Junge O. (2005). A set oriented approach to optimal feedback stabilization. Sys Control Lett 54: 169–180

    Article  MATH  Google Scholar 

  • Junge O. and Osinga H. (2004). A set oriented approach to global optimal control. ESAIM Control Optim Calc Var 10: 259–270

    Article  MATH  MathSciNet  Google Scholar 

  • Komarov V.A. and Pevchikh K.E. (1991). A method of approximating attainability sets for differential inclusions with a prescribed accuracy. USSR Comput Math Math Phys 31(1): 109–112

    MATH  MathSciNet  Google Scholar 

  • Lempio F. and Veliov V. (1998). Discrete approximations of differential inclusions. Bayreuth Math Schr 54: 149–232

    MATH  MathSciNet  Google Scholar 

  • Murray J.D. (1989). Mathematical biology. Springer, Berlin

    MATH  Google Scholar 

  • Szolnoki D. (2003). Set oriented methods for computing reachable sets and control sets. Discrete Contin Dyn Sys Ser B 3(3): 361–382

    Article  MATH  MathSciNet  Google Scholar 

  • Warga J. (1972). Optimal control of differential and functional equations. Academic Press, New York

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to W.-J. Beyn.

Additional information

Supported by CRC 701 “Spectral Analysis and Topological Methods in Mathematics”.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Beyn, WJ., Rieger, J. Numerical fixed grid methods for differential inclusions. Computing 81, 91–106 (2007). https://doi.org/10.1007/s00607-007-0240-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00607-007-0240-4

AMS Subject Classifications

Keywords

Navigation