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Computing Qualitatively Correct Approximations of Balance Laws: Exponential-Fit, Well-Balanced and Asymptotic-Preserving (SEMA SIMAI Springer Series)

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The book gives an overview of recent numerical techniques for the integration of partial differential equations, especially hyperbolic systems of balance laws in one space dimension (Part I) and weakly nonlinear kinetic equations (Part II). Several of its salient features are:

  • Surveys both analytical and numerical aspects of hyperbolic balance laws (including the recent theory of viscosity solutions for systems)
  • Numerous derivations of both well-balanced and asymptotic-preserving schemes emphasizing relations between each other Includes original material about K-multibranch solutions for linear geometric optics or order-preserving strings
  • Several chapters about numerical approximation of chemotaxis or semiconductor kinetic models which display constant macroscopic fluxes at stationary state ("qualitatively correct" approximations)
  • Presents well-balanced techniques for linearized Boltzmann and Fokker-Planck kinetic equations relying on "Caseology" methods.
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