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Description / Table of Contents:
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat
Type of Medium:
Book
Pages:
IX, 369 Seiten
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Diagramme (schwarz-weiß)
Series Statement:
Mathematics in science and engineering Volume 9
DDC:
515.72480113
Language:
English
Note:
Front Cover; Non-Linear Wave Propagation; Copyright Page; Contents; Preface; PART I-GENERAL THEORY; Chapter 1. General Hyperbolic Equations; 1.1 The Wave and Hyperbolic Equations; 1.2 The Cauchy Problem and Characteristics; 1 .3 Mixed Boundary and Initial Value Problems; 1.4 Non-Linear Equations, Quasi-Linear Systems, and Lipschitz Continuous Solutions; 1.5 Systems of Quasi-Linear Equations with Many Variables; 1.6 Quasi-Linear Hyperbolic First Order Systems and Characteristics; 1.7 Rays and Wave Fronts; 1.8 Illustrative Examples: The Maxwell Equations; 1.9 Hydrodynamics
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Chapter 2. The Method of Characteristics; 2.1 Riemann Invariants-Systems with Two Dependent Variables; 2.2 Generalised Riemann Invariants-System with n Dependent Variables; 2.3 Mixed Boundary and Initial Value Problems; 2.4 Propagation of Discontinuities along Wave Fronts; Chapter 3. Conservation Laws and Weak Solutions; 3.1 Conservation Laws; 3.2 Weak Solutions; 3.3 Evolutionary Conditions on Discontinuities in Conservation Laws of Hyperbolic Type; 3.4 Evolutionary Conditions on a General System; 3.5 General Shock Relations; 3.6 Hydrodynamic Discontinuities
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3.7 Numerical Solution of Non-Linear Hyperbolic Systems3.8 The Propagation of Weak Discontinuities along Rays; 3.9 Geometrical Acoustics-The Theory of Weak Shock Waves; PART II-THE APPLICATION TO MAGNETOHYDRODYNAMICS; Chapter 4. The Fundamental Equations and Characteristics; 4.1 Basic Equations and Assumptions; 4.2 The Adiabatic Reversible System and the Lundquist Equations; 4.3 The Characteristic Equations; 4.4 Wave Front Diagram; 4.5 Propagation of Weak Hydromagnetic Discontinuities; Chapter 5. Simple Waves; 5.1 Properties of Magnetic Lines of Force
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5.2 Simple Waves in One-Dimensional PropagationChapter 6. Magnetohydrodynamic Shocks; 6.1 The Conservation Laws; 6.2 Fast and Slow Shocks; 6.3 Limit Shocks; 6.4 Transverse Shocks and Contact Discontinuities; Chapter 7. Interaction of Hydromagnetic Waves; 7.1 Further Considerations on the Evolutionary Condition; 7.2 The Piston Problem; 7.3 Riemann's Problem; Chapter 8. Spatial Discontinuities; 8.1 Weak Discontinuities in Steady Flows; 8.2 The Reducible Form of Plane Aligned-Field Flow; 8.3 Oblique Shock Waves; 8.4 The Discontinuity in the Static Case; Appendices
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A . Basic Theorems in Matrix TheoryB. The Rankine-Hugoniot Relation; C. The Behaviour of F; C. The Behaviour of +- f; D. Shock Relations; E. The Representation of the Hydromagnetic Equations; F. Contact Transformations and the Legendre Transformation; References to Part I; References to Part II; Index;
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