الصفحة 1
الصفحة 1
Numerical Treatment of Partial Differential Equations
In 1988 we started work on the frst German edition of our book, which appeared in 1992. Our aim was to give students a textbook that contained the basic concepts and ideas behind most numerical methods for partial di?er- tial equations. The success of this frst edition and the second edition in 1994 encouraged us, ten years later, to write an almost completely new version, taking into account comments from colleagues and students and drawing on the enormous progress made in the numerical analysis of partial di?erential equations in recent times. The present English version slightly improves the third German edition of 2005: we have corrected some minor errors and added additional material and references.
Hyperbolic Problems : Theory, Numerics, Applications ; Proceedings of the Eleventh International Conference on Hyperbolic Problems held in Ecole Normale Supérieure, Lyon, July 17-21, 2006
This volume contains papers that were presented at HYP2006, the eleventh international Conference on Hyperbolic Problems: Theory, Numerics and Applications held at the Ecole Normale Supérieure de Lyon, France, July 17-21, 2006. This biennial series of conferences has become one of the most important international events in Applied Mathematics. As computers became more and more powerful, the interplay between theory, modelling, and numerical algorithms gained considerable impact, and the scope of HYP conferences expanded accordingly. The field is currently in interaction with a variety of scientific domains, including fluid dynamics, physics, electromagnetism, chemistry, biology, road and network traffic, and engineering. Many of these papers present new effective numerical methods and their application in various contexts.
Jets From Young Stars III : Numerical MHD and Instabilities
This volume contains the lecture notes of the Third JETSET School on Jets from Young Stars focussing on Numerical MHD and Instabilities. The introductory lectures presented here cover the basic concepts of the numerical methods for the integration of hydrodynamic and magnetohydrodynamic equations and of the applications of these methods to the treatment of the instabilities relevant for the physics of stellar jets. The first part of the book contains an introduction to the finite difference and finite volume methods for computing the solutions of hyperbolic partial differential equations and a discussion of approximate Riemann solvers for both hydrodynamic and magnetohydrodynamic problems. The second part is devoted to the discussion of some of the main instability processes that may take place in stellar jets, namely: the Kelvin-Helmholtz, the radiative shock, the pressure driven and the thermal instabilities.
Beyond partial differential equations : On linear and Quasi-Linear abstract hyperbolic evolution equations
The present volume is self-contained and introduces to the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups.
Applicazioni ed esercizi di modellistica numerica per problemi differenziali = Applications and exercises in numerical modeling for differential problems
Contains a collection of exercises related to typical topics in a course on analytical and numerical methods offered in a degree program in Engineering or Mathematics. Starting with exercises in functional analysis and approximation theory, the text develops problems related to the numerical resolution of elliptic, parabolic, and hyperbolic partial differential equations, scalar or vector, in one or more spatial dimensions. Pure diffusion and pure convection problems are therefore addressed, alongside diffusion-transport problems and problems in compressible and incompressible fluid dynamics. Particular emphasis is given to the finite element method for the spatial discretization of the problems considered, although exercises on the finite difference and finite volume methods are also included.
