Skip to main content

Approximations of analytic and differentiable semigroups — Rate of convergence with nonsmooth initial conditions

Part of the Lecture Notes in Mathematics book series (LNM,volume 1076)

Keywords

  • Finite Difference Method
  • Delay Differential Equation
  • Analytic Semigroup
  • Semi Group
  • Galerkin Scheme

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Babuska, I., A. Aziz: The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, Academic Press, New York 1972.

    MATH  Google Scholar 

  2. Banks, H.T., J.A. Burns: Hereditary control problems: Numerical methods based on averaging approximations, SIAM J. Control and Optimization, Vol. 16, No. 2, 1978, pp. 169–208.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Butzer, P.L., H. Berens: Semigroups of Operators and Approximations, Springer Verlag, New York 1967.

    CrossRef  MATH  Google Scholar 

  4. Huang, M., V. Thomee: Some convergence estimates for semidiscrete type schemes for time-dependent nonselfadjoint parabolic equations, Math. of Comp. Vol. 37, 156 (1981), 327–346.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Lasiecka, I.: Convergence Estimates for Semidiscrete Approximations of Nonselfadjoint Parabolic Equations, SIAM Journal on Numerical Analysis, to appear.

    Google Scholar 

  6. Lasiecka, I, A. Manitius: On the smoothing property of Finite Difference Scheme for delay differential equations, manuscript.

    Google Scholar 

  7. Luskin, M., R. Rannacher: On the smoothing property of the Galerkin method for parabolic equations, SIAM J. Numer. Anal., Vol.19, No.1, (1981), 93–113.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations, Lecutes Notes No. 10, Univ. of Maryland.

    Google Scholar 

  9. Sammon, P.M.: Converence estimates for semidiscrete parabolic equation approximations, SIAM J. Numer. Anal. Vol. 19, No. 1, (1982) 68–81.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Taylor, A., D. Lay: Introduction to Functional Analysis, J. Wiley & Sons, New York 1980.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Lasiecka, I. (1984). Approximations of analytic and differentiable semigroups — Rate of convergence with nonsmooth initial conditions. In: Kappel, F., Schappacher, W. (eds) Infinite-Dimensional Systems. Lecture Notes in Mathematics, vol 1076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072772

Download citation

  • DOI: https://doi.org/10.1007/BFb0072772

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13376-6

  • Online ISBN: 978-3-540-38932-3

  • eBook Packages: Springer Book Archive