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.
Numerical partial differential equations for environmental scientists and engineers : A first practical course
This book concerns the practical solution of Partial Differential Equations (PDEs). It reflects an interdisciplinary approach to problems occurring in natural environmental media: the hydrosphere, atmosphere, cryosphere, lithosphere, biosphere and ionosphere. It assumes the reader has gained some intuitive knowledge of PDE solution properties and now wants to solve some for real, in the context of practical problems arising in real situations. The practical aspect of this book is the infused focus on computation. It presents two major discretization methods - Finite Difference and Finite Element. The blend of theory, analysis, and implementation practicality supports solving and understanding complicated problems. It is divided into three parts. Part I is an overview of Finite Difference Methods. Part II focuses on Finite Element Methods, including an FEM tutorial. Part III deals with Inverse Methods, introducing formal approaches to practical problems which are ill-posed.
Numerical Methods and Applications ; 6th International Conference, NMA 2006, Borovets, Bulgaria, August 20-24, 2006, Revised Papers
This book constitutes the thoroughly refereed post-proceedings of the 6th International Conference on Numerical Methods and Applications, NMA 2006. The papers are organized in topical sections on numerical methods for hyperbolic problems, robust preconditioning solution methods, Monte Carlo and quasi-Monte Carlo for diverse applications, metaheuristics for optimization problems, uncertain/control systems and reliable numerics, interpolation and quadrature processes, large-scale computations in environmental modelling, and contributed talks.
Numerical Mathematics and Advanced Applications ; Proceedings of ENUMATH 2005 the 6th European Conference on Numerical Mathematics and Advanced Applications, Santiago de Compostela, Spain, July 2005
This book include applications such as atmosphere and ocean, water pollution, electromagnetism, interface problems, waves, finance, heat transfer, unbounded domains, numerical linear algebra, convection-diffusion, fluid-structure, plates, solids, hyperbolic equations, multiphase flow, Navier-Stokes, singular perturbation problems, non linear PDE, control, parabolic equations, as well as methodologies such as a posteriori error estimates, discontinuous Galerkin methods, multiscale methods, optimization, adaptive methods, domain decomposition techniques, exponential integrators, hp-finite elements, level set methods, fractional step methods, penalty procedures, and finite volumes. The book gives an extensive overview of the most recent research in scientific computing, providing to the reader the latest developments concerning the mathematical issues and the applications of this active field of science.
Nonlinear Parabolic-Hyperbolic Coupled Systems and Their Attractors
This book presents recent results concerning the global existence in time, the large-time behaviour, decays of solutions and the existence of global attractors for some nonlinear parabolic-hyperbolic coupled systems of evolutionary partial differential equations arising from physics, mechanics and material science, such as the compressible Navier-Stokes equations, thermo(visco)elastic systems and elastic systems. To keep the book as self-contained as possible, the first chapter introduces to the needed results and tools from functional analysis, Sobolev spaces, differential and integral inequa.
Non-Euclidean Geometries : János Bolyai Memorial Volume
Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics. This book is intended for those who teach, study, and do research in geometry and history of mathematics. Cultural historians, physicists, and computer scientists will also find it an important source of information.
New Trends in the Theory of Hyperbolic Equations
The present volume is dedicated to modern topics of the theory of hyperbolic equations such as evolution equations, multiple characteristics, propagation phenomena, global existence, influence of nonlinearities. It is addressed to beginners as well as specialists in these fields. The contributions are to a large extent self-contained.
Modellistica numerica per problemi differenziali = Numerical modeling for differential problems
This text introduces the basic concepts for the numerical modeling of partial differential problems. We consider the classic elliptic, parabolic and hyperbolic linear equations, but also other equations, such as those of diffusion and transport, of Navier-Stokes, and the conservation laws, and we provide numerous physical examples underlying these equations. Then we analyze numerical resolution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods. In particular, the algorithmic and computer implementation aspects are discussed and various easy-to-use programs are provided.
Modellistica Numerica per Problemi Differenziali = Numerical Modeling for Differential Problems
This text introduces the fundamental concepts for the numerical modeling of partial differential problems. We consider the classic linear elliptic, parabolic and hyperbolic equations, but also other equations, such as those of diffusion and transport, of Navier-Stokes, and the conservation laws. Numerous physical examples underlying these equations are provided, their main mathematical properties are studied, then numerical resolution methods based on finite elements, finite differences, finite volumes and spectral methods are proposed and analyzed. In particular, the algorithmic and computer implementation aspects are discussed and some easy-to-use programs in C ++ language are provided. The text does not presuppose an advanced mathematical knowledge of partial differential equations: the strictly indispensable concepts in this regard are reported in the Appendix. The volume is therefore suitable for students of scientific degree courses (Engineering, Mathematics, Physics, Chemistry, Information Sciences) and recommended for researchers from the academic and extra-academic world who want to approach this interesting branch of applied mathematics.
Inverse Problems for Partial Differential Equations
The topic of the inverse problems is of substantial and rapidly growing interest for many scientists and engineers. The second edition covers most important recent developments in the field of inverse problems, describing theoretical and computational methods, and emphasizing new ideas and techniques. It also reflects new changes since the first edition, including some corrections. This edition is considerably expanded, with some concepts such as pseudo-convexity, and proofs simplified. New material is added to reflect recent progress in theory of inverse problems.This book is intended for mathematicians working with partial differential equations and their applications, and physicists, geophysicists and engineers involved with experiments in nondestructive evaluation, seismic exploration, remote sensing and tomography.
Introduzione al Calcolo Scientifico : Esercizi e problemi risolti con MATLAB = Introduction to scientific computing : Exercises and problem solved with MATLAB
Introduces the fundamental concepts for the numerical modeling of partial differential problems. We consider the classic linear elliptic, parabolic and hyperbolic equations, but also other equations, such as those of diffusion and transport, of Navier-Stokes, and the conservation laws. Numerous physical examples underlying these equations are provided, their main mathematical properties are studied, then numerical resolution methods based on finite elements, finite differences, finite volumes and spectral methods are proposed and analyzed. In particular, the algorithmic and computer implementation aspects are discussed and some easy-to-use programs in C ++ language are provided. The text does not presuppose an advanced mathematical knowledge of partial differential equations: the strictly indispensable concepts in this regard are reported in the Appendix. THE VOLUME is therefore suitable for students of scientific degree courses (Engineering, Mathematics, Physics, Chemistry, Information Sciences) and recommended for researchers from the academic and extra-academic world who want to approach this interesting branch of applied mathematics.
Introduction to Classical Geometries
This book follows Felix Klein’s proposal of studying geometry by looking at the symmetries (or rigid motions) of the space in question. In this way the classical geometries are studied: Euclidean, affine, elliptic, projective and hyperbolic. For simplicity the focus is on the two-dimensional case, which is already rich enough, though some aspects of the 3- or n-dimensional geometries are included. Once plane geometry is well understood, it is much easier to go into higher dimensions.
Hyperbolic Systems of Balance Laws : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14-21, 2003
The present Cime volume includes four lectures by Bressan, Serre, Zumbrun and Williams and an appendix with a Tutorial on Center Manifold Theorem by Bressan. Bressan’s notes start with an extensive review of the theory of hyperbolic conservation laws. Then he introduces the vanishing viscosity approach and explains clearly the building blocks of the theory in particular the crucial role of the decomposition by travelling waves. Serre focuses on existence and stability for discrete shock profiles, he reviews the existence both in the rational and in the irrational cases and gives a concise introduction to the use of spectral methods for stability analysis. Finally the lectures by Williams and Zumbrun deal with the stability of multidimensional fronts.
Hyperbolic Problems and Regularity Questions
This book discusses new challenges in the quickly developing field of hyperbolic problems. Particular emphasis lies on the interaction between nonlinear partial differential equations, functional analysis and applied analysis as well as mechanics.The book originates from a recent conference focusing on hyperbolic problems and regularity questions. It is intended for researchers in functional analysis, PDE, fluid dynamics and differential geometry.
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.
Hyperbolic Geometry
The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. The basic approach taken is to define hyperbolic lines and develop a natural group of transformations preserving hyperbolic lines, and then study hyperbolic geometry as those quantities invariant under this group of transformations. Topics covered include the upper half-plane model of the hyperbolic plane, Möbius transformations, the general Möbius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the Poincaré disc model, convex subsets of the hyperbolic plane, hyperbolic area, the Gauss-Bonnet formula and its applications.
Hyberbolic Conservation Laws in Continuum Physics
This masterly exposition of the mathematical theory of hyperbolic system for conservation laws brings out the intimate connection with continuum thermodynamics, by emphasising issues in which the analysis may reveal something about the physics and, in return, the underlying physical structure may direct and drive the analysis.Theis edition contains chapter recounting the exciting recent developments on the vanishing viscosity method. Numerous new sections have been incorporated in preexisting chapters, to introduce newly derived results or present older material
Heat Conduction : Mathematical Models and Analytical Solutions
Many phenomena in social, natural and engineering fields are governed by wave, potential, parabolic heat-conduction, hyperbolic heat-conduction and dual-phase-lagging heat-conduction equations. The focus of the present monograph is on these equations: their solution structures, methods of finding their solutions under various supplementary conditions, as well as the physical implication and applications of their solutions.
From Hyperbolic Systems to Kinetic Theory : A Personalized Quest
Equations of state are not always effective in continuum mechanics. Maxwell and Boltzmann created a kinetic theory of gases, using classical mechanics. How could they derive the irreversible Boltzmann equation from a reversible Hamiltonian framework? By using probabilities, which destroy physical reality! Forces at distance are non-physical as we know from Poincaré's theory of relativity. Yet Maxwell and Boltzmann only used trajectories like hyperbolas, reasonable for rarefied gases, but wrong without bound trajectories if the "mean free path between collisions" tends to 0. Tartar relies on his H-measures, a tool created for homogenization, to explain some of the weaknesses, e.g. from quantum mechanics: there are no "particles", so the Boltzmann equation and the second principle, can not apply. He examines modes used by energy, proves which equation governs each mode, and conjectures that the result will not look like the Boltzmann equation, and there will be more modes than those indexed by velocity!
Foundations of Hyperbolic Manifolds
The book is divided into three parts. The first part is concerned with hyperbolic geometry and discrete groups. The main results are the characterization of hyperbolic reflection groups and Euclidean crystallographic groups. The second part is devoted to the theory of hyperbolic manifolds. The main results are Mostow’s rigidity theorem and the determination of the global geometry of hyperbolic manifolds of finite volume. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. The main result is Poincare«s fundamental polyhedron theorem.
