Grossmann, C. et al.
Numerical Treatment of Partial Differential Equations
Springer-Verlag 2007.
596 pp.(P)
ISBN 3-540-71582-7
9,800円
Translation and Revision of the 3rd edition of "Numerische Behandlung partieller Differentialgleichungen" published by Teubner, 2005
Contents
Part.1: Basics: 1.1 Classification and Correctness/ 1.2 Fourier’s Method, Integral Transforms/ 1.3 Maximum Principle, Fundamental Solution/ Part.2: Finite Difference Methods: 2.1 Basic Concepts/ 2.2 Illustrative Examples/ 2.3 Transportation Problems and Conservation Laws/ 2.4 Elliptic Boundary Value Problems/ 2.5 Finite Volume Methods as Finite Difference Schemes/ 2.6 Parabolic Initial-Boundary Value Problems/ 2.7 Second-Order Hyperbolic Problems/ Part.3: Weak Solutions: 3.1 Introduction/ 3.2 Adapted Function Spaces/ 3.3 Variational Equations and Conforming Approximation/ 3.4 Weakening V-ellipticity/ 3.5 Nonlinear Problems/ Part.4: The Finite Element Method: 4.1 A First Example/ 4.2 Finite-Element-Spaces/ 4.3 Practical Aspects of the Finite Element Method/ 4.4 Convergence of Conforming Methods/ 4.5 Nonconforming Finite Element Methods/ 4.6 Mixed Finite Elements/ 4.7 Error Estimators and Adaptive FEM/ 4.8 The Discontinuous Galerkin Method/ 4.9 Further Aspects of the Finite Element Method/ Part.5: Finite Element Methods for Unsteady Problems: 5.1 Parabolic Problems/ 5.2 Second-Order Hyperbolic Problems/ Part.6: Singularly Perturbed Boundary Value Problems: 6.1 Two-Point Boundary Value Problems/ 6.2 Parabolic Problems, One-dimensional in Space/ 6.3 Convection-Diffusion Problems in Several Dimensions/ Part.7: Variational Inequalities, Optimal Control: 7.1 Analytic Properties/ 7.2 Discretization of Variational Inequalities/ 7.3 Penalty Methods/ 7.4 Optimal Control of PDEs/ Part.8: Numerical Methods for Discretized Problems: 8.1 Some Particular Properties of the Problems/ 8.2 Direct Methods/ 8.3 Classical Iterative Methods/ 8.4 The Conjugate Gradient Method/ 8.5 Multigrid Methods/ 8.6 Domain Decomposition, Parallel Algorithms/ Bibliography: Textbooks and Monographs/ Bibliography: Original Papers/ Index/ *
Kotelenez, P.
Stochastic Ordinary and Stochastic Partial Differential Equations
Transition from Microscopic to Macroscopic Equations
Springer-Verlag 2007.11
460 pp.(H)
ISBN 0-387-74316-2
9,400円
Contents
Part I: From Microscopic Dynamics to Mesoscopic Kinematics: 1. Heuristics: Microscopic Model and Space-Time Scales/ 2. Deterministic Dynamics in a Lattice Model and a Mesoscopic (Stochastic) Limit/ 3. Proof of the Mesoscopic Limit Theorem/ Part II: Mesoscopic A: Stochastic Ordinary Differential Equations: 4. Stochastic Ordinary Differential Equations: Existence, Uniqueness, and Flows Properties/ 5. Qualitative Behavior of Correlated Brownian Motions/ 6. Proof of the Flow Property/ 7. Comments on SODEs: A Comparison with Other Approaches/ Part III: Mesoscopic B: Stochastic Partial Differential Equations: 8. Stochastic Partial Differential Equations: Finite Mass and Extensions/ 9. Stochastic Partial Differential Equations: Infinite Mass/ 10. Stochastic Partial Differential Equations: Homogeneous and Isotropic Solutions/ 11. Proof of Smoothness, Integrability, and Ito's Formula/ 12 Proof of Uniqueness / 13. Comments on Other Approaches to SPDEs/ Part IV: Macroscopic: Deterministic Partial Differential Equations: 14. Partial Differential Equations as a Macroscopic Limit/ Part V: General Appendix: 15 Appendix/ Subject Index/ *
Elaydi, S. et al. ed.
Difference Equations, Special Functions and Orthgonal Polynomials
World Scientific Pub., SGP 2007.5
778 pp.(H)
ISBN 981-270-643-7
25,400円
Proceedings of the International Conference Munich, Germany 25 - 30 July 2005
Contents
1.Pascal Matrix, Classical Polynomials and Difference Equations (L Aceto & D Trigiante)/ 2.Logarithmic Order and Type of Indeterminate Moment Problems (C Berg & H L Pedersen)/ 3.A System of Biorthogonal Trigonometric Polynomials (E Berriochoa et al.)/ 4.On Two Problems in Lacunary Polynomial Interpolation (M G de Bruin)/ 5.A Myriad of Sierpinski Curve Julia Sets (R L Devaney)/ 6.The Comparative Index for Conjoined Bases of Symplectic Difference Systems (J V 7.A Renaissance for a q-Umbral Calculus (T Ernst)/ 7.Fourth-Order Bessel-Type Special Functions: A Survey (W N Everitt)/ 8.On the Asymptotic Behavior of Solutions of Neuronic Difference Equations (Y Hamaya)/ 9.Computer Algebra Methods for Orthogonal Polynomials (W Koepf)/ 10.RiemannHilbert Problem for a Generalized Nikishin System (A F Moreno)/ 11.Ideal Turbulence and Problems of Its Visualization (A N Sharkovsky)/ 12.Fine Structure of the Zeros of Orthogonal Polynomials: A Review (B Simon)/ 13.(2+1) Dimensional Lattice Hierarchies Derived from Discrete Operator Zero Curvature Equation (Z-N Zhu)/ and other papers/
* This volume contains talks given at a joint meeting of three communities working in the fields of difference equations, special functions and applications (ISDE, OPSFA, and SIDE). The articles reflect the diversity of the topics in the meeting but have difference equations as common thread. Articles cover topics in difference equations, discrete dynamical systems, special functions, orthogonal polynomials, symmetries, and integrable difference equations. *
Berestycki, H. et al. ed.
Perspectives in Nonlinear Partial Differential Equations
In Honor of Haim Brezis
AMS 2007.
494 pp. (P)
ISBN 0-8218-4190-4
19,400円
Contents
1.Concentration phenomena for Nonlinear Schrodinger Equations: recent results and new perspectives/ 2.On the chain rule for the divergence of BV-like vector fields: applications, partial results, open problems/ 3.Compactness/ 4. Generalized travelling waves for reaction-diffusion equations/ 5.Some questions related to the lifting problem in Sobolev spaces/ 6.Normal forms and the nonlinear Schrodinger equation/ 7.Extremal solutions and instantaneous complete blow-up for elliptic and parabolic problems/ 8.Capillary drops on an inhomogeneous surface/ 9.Diffusive Lagrangian transformations, Navier-Stokes equations and applications/ 10.Some open problems on the control of nonlinear partial differential equations/ 11.The 1-Laplacian, the ∞-Laplacian and differential games/ 12.Probabilistic approach to a class of semilinear Partial differentions/ 13.Variational methods in image processing/ 14.Null hypersurfaces with finite curvature fiux and a breakdown criterion in general relativity/ 15.Some Liouville theorems and applications/ 16.Analysis on Faddeev knots and Skyrme solitons: recent progress and open problems/ 17.The precise boundary trace of positive solutions of the equation △u＝uq in the supercritial case/ 18.Blow-up in nonlinear heat equations with supercritical power nonlinearity/ 19.Sobolev maps on manifolds: degree, approximation,lifting/ 20.Partial and full symmetry of solutions of quasilinear elliptic equations via the comparison principle/ 21.Single and multi-transition solutions of a family of PDE's/ 22.Some methods and issues in the dynamics of vortices in the parabolic Ginzburg-Landau equations/ 23.Piblications of Haim Brezis/ *
Jordan, D. & Smith, P.
Nonlinear Ordinary Differential Equations 4th ed.
An Introduction for Scientists and Engineers
Oxford U.P. 2007.10
544 pp. (P)
ISBN 0-19-920825-5
9,200円
Contents
Preface / 1. Second-order differential equations in the phase plane / 2. Plane autonomous systems and linearization / 3. Geometrical aspects of plane autonomous systems / 4. Periodic solutions; averaging methods / 5. Perturbation methods / 6. Singular perturbation methods / 7. Forced oscillations: harmonic and subharmonic response, stability, and entrainment / 8. Stability / 9. Stability by solution perturbation: Mathieu's equation / 10. Liapurnov methods for determining stability of the zero solution / 11. The existence of periodic solutions / 12. Bifurcations and manifolds / 13. Poincar sequences, homoclinic bifurcation, and chaos / Answers to the exercises / Appendices / References and further reading / Index / *
* This is a thoroughly updated and expanded 4th edition of the classic text Nonlinear Ordinary Differential Equations by Dominic Jordan and Peter Smith. Including numerous worked examples and diagrams, further exercises have been incorporated into the text and answers are provided at the back of the book. Topics include phase plane analysis, nonlinear damping, small parameter expansions and singular perturbations, stability, Liapunov methods, Poincare sequences, homoclinic bifurcation and Liapunov exponents. *
720-35 登録日 08.01.28
