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Some fundamental tools

  • Luca Formaggia
  • Fausto Saleri
  • Alessandro Veneziani
Part of the UNITEXT book series (UNITEXT)

Abstract

Mathematical modeling of real-life problems in engineering, physics or life sciences often gives rise to partial differential problems that cannot be solved analytically but need a numerical scheme to obtain a suitable approximation. Dealing with numerical modeling requires first of all an understanding of the underlying differential problem. The type of differential problem, as well as issues of well-posedness and regularity of the solution may indeed drive the selection of the appropriate simulation tool. A second requirement is the analysis of numerical schemes, in particular their stability and convergence characteristics. Last, but not least, numerical schemes must be implemented in a computer language, and often aspects which look easy “on paper” arise complex implementation issues, particularly when computational efficiency is at stake.

Keywords

Sobolev Space Numerical Scheme Dual Space Real Vector Space Left Eigenvector 
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.

Copyright information

© Springer-Verlag Italia 2012

Authors and Affiliations

  • Luca Formaggia
    • 1
  • Fausto Saleri
    • 1
  • Alessandro Veneziani
    • 2
  1. 1.MOX — Dipartimento di Matematica “F. Brioschi”Politecnico di MilanoItaly
  2. 2.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA

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