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Differential Equations in Technology and Medicine. Computational Concepts, Adaptive Algorithms, and Virtual Labs

Please always quote using this URN: urn:nbn:de:0297-zib-4223
  • This series of lectures has been given to a class of mathematics postdocs at a European summer school on Computational Mathematics Driven by Industrial Applications in Martina Franca, Italy (organized by CIME). It deals with a variety of challenging real life problems selected from clinical cancer therapy, communication technology, polymer production, and pharmaceutical drug design. All of these problems from rather diverse application areas share two common features: (a) they have been modelled by various differential equations -- elliptic, parabolic, or Schrödinger--type partial differential equations, countable ordinary diffential equations, or Hamiltonian systems, (b) their numerical solution has turned out to be real challenge to computational mathematics.

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Metadaten
Author:Peter Deuflhard
Document Type:ZIB-Report
Tag:adaptive; countable; differential equations:; finite element methods:; grid generation; hamiltonian; medical t; multilevel; ordinary; partial
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65-02 Research exposition (monographs, survey articles)
65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C05 Monte Carlo methods
65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C20 Models, numerical methods [See also 68U20]
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors
65-XX NUMERICAL ANALYSIS / 65Jxx Numerical analysis in abstract spaces / 65J10 Equations with linear operators (do not use 65Fxx)
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L05 Initial value problems
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L08 Improperly posed problems
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N25 Eigenvalue problems
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N55 Multigrid methods; domain decomposition
78-XX OPTICS, ELECTROMAGNETIC THEORY (For quantum optics, see 81V80) / 78Axx General / 78A50 Antennas, wave-guides
Date of first Publication:1999/09/21
Series (Serial Number):ZIB-Report (SC-99-34)
ZIB-Reportnumber:SC-99-34
Published in:Appeared in: Computational Mathematics Driven by Industrial Problems. Springer 2000. Lecture Notes in Mathematics, 1739, pp. 69-125
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