Skip to main content

Abstract

We discuss here the main topics developed in this monograph. Through our analysis, examples and calculations, we show that spectral methods present various advantages in relation to the methods based on finite differences in terms of accuracy, convergence, time of computation and stability.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • 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

Institutional subscriptions

References

  1. B.D. Shizgal, Spectral Methods in Chemistry and Physics. Applications to Kinetic Theory and Quantum Mechanics (Springer, Dordrecht, 2015)

    MATH  Google Scholar 

  2. L.N. Trefethen, Spectral Methods in MATLAB (SIAM, Philadelphia, 2000)

    Book  Google Scholar 

  3. D. Gottlieb, S.A. Orszag, Numerical Analysis of Spectral Methods (SIAM, Philadelphia, 1977)

    Book  Google Scholar 

  4. B. Fornberg, A Practical Guide to Pseudospectral Methods. Cambridge Monographs on Applied and Computational Mathematics (Cambridge University Press, Cambridge, 1998)

    Google Scholar 

  5. J.P. Boyd, Chebyshev and Fourier Spectral Methods (Dover, New York, 2001)

    MATH  Google Scholar 

  6. G. Ben-Yu, Spectral Methods and Their Applications (World Scientific, Singapore, 1998)

    Book  Google Scholar 

  7. D.A. Kopriva, Implementing Spectral Methods for Partial Differential Equations Algorithms for Scientists and Engineers (Springer, Berlin, 2009)

    Book  Google Scholar 

  8. R.J. Randall, Finite Difference Methods for Ordinary and Partial Differential Equations, Steady State and Time Dependent Problems (SIAM, Philadelphia, 2007)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Victo dos Santos Filho .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Rawitscher, G., dos Santos Filho, V., Peixoto, T.C. (2018). Conclusions. In: An Introductory Guide to Computational Methods for the Solution of Physics Problems. Springer, Cham. https://doi.org/10.1007/978-3-319-42703-4_13

Download citation

Publish with us

Policies and ethics