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  • Books  (57)
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  • Berlin [u.a.] : Springer  (57)
  • 2000-2004  (57)
  • 1995-1999
  • 2004  (27)
  • 2003  (30)
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  • Books  (57)
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  • 2000-2004  (57)
  • 1995-1999
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  • 1
    Monograph available for loan
    Monograph available for loan
    Random dynamical systems (2003)
    Berlin [u.a.] : Springer
    Details Availability
    Call number: PIK M 370-08-0250
    Description / Table of Contents: Contents: Chapter 1. Basic Definitions. Invariant Measures; Chapter 2. Generation; Chapter 3. The Multiplicative Ergodic Theorem in Euclidean Space; Chapter 4. The Multiplicative Ergodic Theorem on Bundles and Manifolds; Chapter 5. The MET for Related Linear and Affine RDS; Chapter 6. RDS on Homogeneous Spaces of the General Linear Group; Chapter 7. Invariant Manifolds; Chapter 8. Normal Forms; Chapter 9. Bifurcation Theory; Appendix A. Measurable Dynamical Systems; Appendix B. Smooth Dynamical Systems
    Type of Medium: Monograph available for loan
    Pages: XV, 586 S. : graph. Darst.
    Edition: Corr. 2. printing
    ISBN: 3540637583
    Series Statement: Springer Monographs in Mathematics
    Location: A 18 - must be ordered
    Branch Library: PIK Library
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  • 2
    Monograph available for loan
    Monograph available for loan
    Numerical solution of time-dependent advection-diffusion-reaction equations (2003)
    Berlin [u.a.] : Springer
    Associated volumes
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    Call number: AWI S3-08-0024
    In: Springer series in computational mathematics, 33
    Description / Table of Contents: This book descibes numerical methods for partial differential equations (PDEs) coupling advection, diffusion and reaction terms,encompassing methods for hyperbolic, parabolic and stiff and nonstiff ordinary differential equations (ODEs). The emphasis lies on time-dependent transport-chemistry problems, describing e.g. the evolution of concentrations in environmental and biological applications. Along with the common topics of stability and convergence, much attention is paid on how to prevent spurious, negative concentrations and oscillations, both in space and time. Many of the theoretical aspects are illustrated by numerical experiments on models from biology, chemistry and physics. A unified approach is followed by emphasizing the method of lines or semi-discretization. In this regard this book differs substantially from more specialized textbooks which deal exclusively with either PDEs or ODEs. This book treats integration methods suitable for both classes of problems and thus is of interest to PDE researchers unfamiliar with advanced numerical ODE methods, as well as to ODE researchers unaware of the vast amount of interesting results on numerical PDEs.
    Type of Medium: Monograph available for loan
    Pages: X, 471 S. : graph. Darst.
    Edition: corr. 2. print.
    ISBN: 978-3-540-03440-7
    Series Statement: Springer series in computational mathematics 33
    Note: Table of Contents: I BASIC CONCEPTS AND DISCRETIZATIONS. - 1 Advection-Diffusion-Reaction Equations. - 1.1 Nonlinear Reaction Problems from Chemistry. - 1.2 Model Equations for Advection-Diffusion. - 1.3 Multi-dimensional Problems. - 1.4 Examples of Applications. - 2 Basic Discretizations for ODEs. - 2.1 Initial Value Problems and Euler's Method. - 2.2 Norms and Matrices. - 2.3 Perturbations on ODE Systems. - 2.4 The θ-Method and Stiff Problems. - 2.5 Stability of the θ-Method. - 2.6 Consistency and Convergence of the θ-Method. - 2.7 Nonlinear Results for the θ-Method. - 2.8 Concluding Remarks. - 3 Basic Spatial Discretizations. - 3.1 Discrete Fourier Decompositions. - 3.2 The Advection Equation. - 3.3 The Diffusion Equation. - 3.4 The Advection-Diffusion Equation. - 4 Convergence of Spatial Discretizations. - 4.1 Stability, Consistency and Convergence. - 4.2 Advection-Diffusion with Constant Coefficients. - 4.3 Advection with Variable Coefficients. - 4.4 Diffusion with Variable Coefficients. - 4.5 Variable Coefficients and Higher-Order Schemes. - 5 Boundary Conditions and Spatial Accuracy. - 5.1 Refined Global Error Estimates. - 5.2 Outflow with Central Advection Discretization. - 5.3 Boundary Conditions with the Heat Equation. - 5.4 Boundary Conditions and Higher-Order Schemes. - 6 Time Stepping for PDEs. - 6.1 The Method of Lines and Direct Discretizations. - 6.2 Stability, Consistency and Convergence. - 6.3 Stability for MOL - Stability Regions. - 6.4 Von Neumann Stability Analysis. - 7 Monotonicity Properties. - 7.1 Positivity and Maximum Principle. - 7.2 Positive Semi-discrete Systems. - 7.3 Positive Time Stepping Methods. - 7.4 Numerical Illustrations. - 8 Numerical Test Examples. - 8.1 The Nonlinear Schrödinger Equation. - 8.2 The Angiogenesis Model. - II TIME INTEGRATION METHODS. - 1 Runge-Kutta Methods. - 1.1 The Order Conditions. - 1.2 Examples. - 1.3 The Stability Function. - 1.4 Step Size Restrictions for Advection-Diffusion. - 1.5 Rosenbrock Methods. - 2 Convergence of Runge-Kutta Methods. - 2.1 Order Reduction. - 2.2 Local Error Analysis. - 2.3 Global Error Analysis. - 2.4 Concluding Notes. - 3 Linear Multistep Methods. - 3.1 The Order Conditions. - 3.2 Examples. - 3.3 Stability Analysis. - 3.4 Step Size Restrictions for Advection-Diffusion. - 3.5 Convergence Analysis. - 4 Monotone ODE Methods. - 4.1 Linear Positivity for One-Step Methods. - 4.2 Nonlinear Positivity for One-Step Methods. - 4.3 Positivity for Multistep Methods. - 4.4 Related Monotonicity Results. - 5 Variable Step Size Control. - 5.1 Step Size Selection. - 5.2 An Explicit Runge-Kutta Example. - 5.3 An Implicit Multistep Example. - 5.4 General Purpose ODE Codes. - 6 Numerical Examples. - 6.1 A Model for Antibodies in Tumorous Tissue. - 6.2 The Nonlinear Schrödinger Equation. - III ADVECTION-DIFFUSION DISCRETIZATIONS. - 1 Non-oscillatory MOL Advection Discretizations. - 1.1 Spatial Discretization for Linear Advection. - 1.2 Numerical Examples. - 1.3 Positivity and the TVD Property. - 1.4 Nonlinear Scalar Conservation Laws. - 2 Direct Space-Time Advection Discretizations. - 2.1 Optimal-Order DST Schemes. - 2.2 A Non-oscillatory Third-Order DST Scheme. - 2.3 Explicit Schemes with Unconditional Stability. - 3 Implicit Spatial Discretizations. - 3.1 Order Conditions. - 3.2 Examples. - 3.3 Stability and Convergence. - 3.4 Monotonicity. - 3.5 Time Integration Aspects. - 4 Non-uniform Grids - Finite Volumes (1D). - 4.1 Vertex Centered Schemes. - 4.2 Cell Centered Schemes. - 4.3 Numerical Illustrations. - 4.4 Higher-Order Methods and Limiting. - 5 Non-uniform Grids - Finite Elements (1D). - 5.1 The Basic Galerkin Method. - 5.2 Standard Galerkin Error Estimates. - 5.3 Upwinding. - 6 Multi-dimensional Aspects. - 6.1 Cartesian Grid Discretizations. - 6.2 Diffusion on Cartesian Grids. - 6.3 Advection on Cartesian Grids. - 6.4 Transformed Cartesian Grids. - 6.5 Unstructured Grids. - 7 Notes on Moving Grids and Grid Refinement. - 7.1 Dynamic Regridding. - 7.2 Static Regridding. - IV SPLITTING METHODS. - 1 Operator Splitting. - 1.1 First-Order Splitting. - 1.2 Second-Order Symmetrical Splitting. - 1.3 Higher-Order Splittings. - 1.4 Abstract Initial Value Problems. - 1.5 Advection-Diffusion-Reaction Splittings. - 1.6 Dimension Splitting. - 1. 7 Boundary Values and Stiff Terms. - 2 LOD Methods. - 2.1 The LOD-Backward Euler Method. - 2.2 LOD Crank-Nicolson Methods. - 2.3 The Trapezoidal Splitting Method. - 2.4 Boundary Correction Techniques. - 2.5 Numerical Comparisons. - 3 ADI Methods. - 3.1 The Peaceman-Rachford Method. - 3.2 The Douglas Method. - 4 IMEX Methods. - 4.1 The IMEX-θ Method. - 4.2 IMEX Multistep Methods. - 4.3 Notes on IMEX Runge-Kutta Methods. - 4.4 Concluding Remarks and Tests. - 5 Rosenbrock AMF Methods. - 5.1 One-Stage Methods of Order One and Two. - 5.2 Two-Stage Methods of Order Two and Three. - 5.3 A Three-Stage Method of Order Two. - 5.4 Concluding Remarks and Tests. - 6 Numerical Examples. - 6.1 Two Chemo-taxis Problems from Biology. - 6.2 The Numerical Methods. - 6.3 Numerical Experiments. - V STABILIZED EXPLICIT RUNGE-KUTTA METHODS. - 1 The RKC Family. - 1.1 Stability Polynomials. - 1.2 Integration Formulas. - 1.3 Internal Stability and Full Convergence Properties. - 2 The ROCK Family. - 2.1 Stability Polynomials. - 2.2 Integration Formulas. - 2.3 Internal Stability and Convergence. - 3 Numerical Examples. - 3.1 A Combustion Model. - 3.2 A Radiation-Diffusion Model. - Bibliography. - Index.
    Location: AWI Reading room
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  • 3
    Monograph available for loan
    Monograph available for loan
    Synchrotron radiation : with 7 tables (2003)
    Berlin [u.a.] : Springer
    Associated volumes
    Details Availability
    Call number: 16/M 03.0375
    In: Pattern recognition approach to data interpretation
    Type of Medium: Monograph available for loan
    Pages: XIII, 274 S.
    ISBN: 3540433929
    Series Statement: Advanced texts in physics
    Classification:
    Physics
    Location: Reading room
    Branch Library: GFZ Library
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  • 4
    Monograph available for loan
    Monograph available for loan
    Stochastic differential equations : an introduction with applications (2003)
    Berlin [u.a.] : Springer
    Details Availability
    Call number: 19/M 04.0077
    Type of Medium: Monograph available for loan
    Pages: XXIII, 360 S.
    Edition: 6th ed.
    ISBN: 3540047581
    Series Statement: Universitext
    Classification:
    Informatics
    Location: Upper compact magazine
    Branch Library: GFZ Library
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  • 5
    Monograph available for loan
    Monograph available for loan
    The climate in historical times : towards a synthesis of holocene proxy data and climate models (2004)
    Berlin [u.a.] : Springer
    Details Availability
    Call number: AWI G5-04-0037 ; 12/M 04.0388 ; 12/M 04.0389 ; M 04.0390 ; M 07.0246
    Description / Table of Contents: The project "Climate in Historical Times" (KIHZ) represents an integrative approach by geoscientists and climate modellers to analyse the dynamics of natural climate variability during the Holocene. This volume summarises the outcome of a KIHZ summer school. The meeting dealt with a variety of topics related to natural climate variability, ranging from reconstructions of past climate using so-called "proxy data" derived from ice cores, lake sediments, tree rings and corals. These data are used to validate and assimilate climate models. The first part of this volume provides an overview of the climate system and its dynamics. It uses climate models of differing complexity and the resources of different archives in order to reconstruct past climate. The second part describes the latest achievements of the KIHZ members in their endeavours to reconstruct past climate by using proxy data, statistical analyses and climate models.
    Type of Medium: Monograph available for loan
    Pages: XXI, 487 S. , Ill., graph. Darst., Kt.
    ISBN: 3540206019
    Series Statement: GKSS School of Environmental Research
    Classification:
    Meteorology and Climatology
    Location: Reading room
    Location: Upper compact magazine
    Location: Upper compact magazine
    Location: Upper compact magazine
    Branch Library: AWI Library
    Branch Library: GFZ Library
    Branch Library: GFZ Library
    Branch Library: GFZ Library
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  • 6
    Monograph available for loan
    Monograph available for loan
    Continuum methods of physical modeling : continuum mechanics, dimensional analysis, turbulence ; with 14 tables (2004)
    Berlin [u.a.] : Springer
    Details Availability
    Call number: 16/M 04.0255
    Description / Table of Contents: The book unifies classical continuum mechanics and turbulence modeling, i.e. the same fundamental concepts are used to derive model equations for material behaviour and turbulence closure and complements these with methods of dimensional analysis. The intention is to equip the reader with the ability to understand the complex nonlinear modeling in material behaviour and turbulence closure as well as to derive or invent his own models. Examples are mostly taken from environmental physics and geophysics.
    Type of Medium: Monograph available for loan
    Pages: XV, 635 S. , Ill
    ISBN: 3540206191
    Series Statement: Physics and astronomy online library
    Classification:
    Mathematics
    Location: Upper compact magazine
    Branch Library: GFZ Library
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  • 7
    Monograph available for loan
    Monograph available for loan
    Multivariate Analysemethoden : eine anwendungsorientierte Einführung (2003)
    Berlin [u.a.] : Springer
    Associated volumes
    Details Availability
    Call number: PIK M 311-04-0108
    In: Springer-Lehrbuch
    Type of Medium: Monograph available for loan
    Pages: XI, 818 S , Ill., graph. Darst
    Edition: 10., neu bearb. und erw. Aufl
    ISBN: 3540004912
    Series Statement: Springer-Lehrbuch
    Location: A 18 - must be ordered
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  • 8
    Monograph available for loan
    Monograph available for loan
    Welt im Wandel: Energiewende zur Nachhaltigkeit (2003)
    Berlin [u.a.] : Springer
    Associated volumes
    Details Availability
    Call number: PIK N 076-03-0253 ; AWI P1-03-0020
    In: Jahresgutachten
    Type of Medium: Monograph available for loan
    Pages: XXIV, 260 S.
    ISBN: 3540401601
    Series Statement: Jahresgutachten / Wissenschaftlicher Beirat der Bundesregierung Globale Umweltveränderungen
    Location: A 18 - must be ordered
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  • 9
    Monograph available for loan
    Monograph available for loan
    Paleoclimate, global change and the future : with 4 tables (2003)
    Berlin [u.a.] : Springer
    Details Availability
    Call number: 12/M 03.0295
    Type of Medium: Monograph available for loan
    Pages: XIV, 220 S.
    ISBN: 3540424024
    Series Statement: Global change - the IGBP series
    Classification:
    Meteorology and Climatology
    Location: Reading room
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  • 10
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    Monograph available for loan
    Remote sensing geology : with 53 tables (2003)
    Berlin [u.a.] : Springer
    Details Availability
    Call number: 7/M 03.0446
    Type of Medium: Monograph available for loan
    Pages: XX, 655 S.
    Edition: 2nd ed.
    ISBN: 3540431853
    Classification:
    Photogrammetry, Remote Sensing
    Location: Reading room
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