Encyclopedia of Applied and Computational Mathematics

Table of Contents

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   Book Overview
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   Chapter 1 Camassa–Holm Equations
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   Chapter 2 Adjoint Methods as Applied to Inverse Problems
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   Chapter 7 Boundary Control Method
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   Chapter 9 Invisibility Cloaking
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   Chapter 13 Elastography, Applications Using MRI Technology
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   Chapter 17 Factorization Method in Inverse Scattering
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   Chapter 19 Inhomogeneous Media Identification
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   Chapter 21 Inverse Spectral Problems: 1-D, Theoretical Results
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    Chapter 24 Inverse Boundary Problems for Electromagnetic Waves
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    Chapter 29 Inverse Nodal Problems: 1-D
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    Chapter 33 Inverse Spectral Problems: 1-D, Algorithms
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    Chapter 37 Linear Sampling
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    Chapter 38 Agent-Based Models in Infectious Disease and Immunology
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    Chapter 43 Optical Tomography: Applications
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    Chapter 44 Optical Tomography: Theory
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    Chapter 45 Inverse Optical Design
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    Chapter 46 Photonic Crystals and Waveguides: Simulation and Design
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    Chapter 48 Radar Imaging
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    Chapter 50 Random Media in Inverse Problems, Theoretical Aspects
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    Chapter 52 Regularization of Inverse Problems
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    Chapter 56 Molecular Dynamics
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    Chapter 60 Actin Cytoskeleton, Multi-scale Modeling
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    Chapter 62 Angiogenesis, Mathematical Modeling Perspective
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    Chapter 63 Applied Control Theory for Biological Processes
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    Chapter 66 Medical Imaging
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    Chapter 67 Cancer Initiation and Progression, Modeling
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    Chapter 68 Cell Biology Modeling Development
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    Chapter 69 Cell Migration, Biomechanics
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    Chapter 70 Cell-Based Modeling
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    Chapter 73 Heart Modeling
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    Chapter 75 Molecular Motor Dynamics, Modeling
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    Chapter 76 Moving Boundary Problems and Cancer
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    Chapter 78 Pattern Formation and Development
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    Chapter 82 Microlocal Analysis Methods
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    Chapter 83 Biofilm Structure and Function, Modeling
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    Chapter 84 Neural Spikes, Identification from a Multielectrode Array
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    Chapter 85 Epidemiology Modeling
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    Chapter 88 Molecular Dynamics Simulations
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    Chapter 90 Metabolic Networks, Modeling
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    Chapter 92 Computerized Tomography, ART
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    Chapter 94 Backward Differentiation Formulae
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    Chapter 96 Boundary Value Methods: GAMD, TOM
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    Chapter 98 Encyclopedia of Applied and Computational Mathematics
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    Chapter 100 Explicit Stabilized Runge–Kutta Methods
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    Chapter 102 Collocation Methods
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    Chapter 103 Composition Methods
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    Chapter 105 Defect Correction Methods
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    Chapter 106 Delay Differential Equations
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    Chapter 107 Dense Output
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    Chapter 110 Electrical Circuits
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    Chapter 111 Euler Methods, Explicit, Implicit, Symplectic
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    Chapter 112 Exponential Integrators
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    Chapter 114 Fer and Magnus Expansions
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    Chapter 115 Gauss Methods
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    Chapter 116 General Linear Methods
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    Chapter 117 Hamiltonian Systems
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    Chapter 118 Heterogeneous Multiscale Methods for ODEs
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    Chapter 120 Index Concepts for Differential-Algebraic Equations
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    Chapter 121 Initial Value Problems
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    Chapter 122 Lie Group Integrators
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    Chapter 123 Lobatto Methods
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    Chapter 124 Mechanical Systems
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    Chapter 126 Chebyshev Polynomials
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    Chapter 128 Multistep Methods
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    Chapter 129 Nyström Methods
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    Chapter 130 One-Step Methods, Order, Convergence
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    Chapter 132 Order Conditions and Order Barriers
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    Chapter 134 Order Stars and Stability Domains
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    Chapter 135 Oscillatory Problems
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    Chapter 139 Radau Methods
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    Chapter 155 Modeling of Blood Clotting
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    Chapter 156 Distributions and the Fourier Transform
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    Chapter 157 Interferometric Imaging and Time Reversal in Random Media
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    Chapter 158 Inversion Formulas in Inverse Scattering
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    Chapter 161 Computational Mechanics
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    Chapter 162 Angiogenesis, Computational Modeling Perspective
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    Chapter 173 Complexity of Computational Problems in Exact Linear Algebra
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    Chapter 192 Finite Fields
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    Chapter 201 Logical Characterizations of Complexity Classes
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    Chapter 204 Markov Random Fields in Computer Vision: MAP Inference and Learning
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    Chapter 212 Property Testing
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    Chapter 231 Logarithmic Norms
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    Chapter 233 Exact Wavefunctions Properties
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    Chapter 234 Density Functional Theory
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    Chapter 236 Hartree–Fock Type Methods
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    Chapter 237 Post-Hartree-Fock Methods and Excited States Modeling
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    Chapter 238 Linear Time Independent Reaction Diffusion Equations: Computation
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    Chapter 239 Molecular Geometry Optimization, Models
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    Chapter 240 Relativistic Theories for Molecular Models
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    Chapter 241 Relativistic Models for the Electronic Structure of Atoms and Molecules
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    Chapter 242 Classical Iterative Methods
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    Chapter 243 Nuclear Modeling
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    Chapter 245 Numerical Approaches for High-Dimensional PDEs for Quantum Chemistry
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    Chapter 246 Coupled-Cluster Methods
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    Chapter 247 Quantum Monte Carlo Methods in Chemistry
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    Chapter 248 Finite Element Methods for Electronic Structure
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    Chapter 249 Finite Difference Methods in Electronic Structure Calculations
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    Chapter 250 Programming Languages for Scientific Computing
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     Chapter 252 Linear Scaling Methods
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     Chapter 253 Large-Scale Electronic Structure and Nanoscience Calculations
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     Chapter 254 Fast Methods for Large Eigenvalues Problems for Chemistry
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     Chapter 255 A Priori and A Posteriori Error Analysis in Chemistry
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     Chapter 257 Quantum Time-Dependent Problems
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     Chapter 258 Numerical Analysis of Eigenproblems for Electronic Structure Calculations
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     Chapter 260 Born–Oppenheimer Approximation, Adiabatic Limit, and Related Math. Issues
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     Chapter 261 Liquid-Phase Simulation: Theory and Numerics of Hybrid Quantum-Mechanical/Classical Approaches
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     Chapter 262 Mathematical Theory for Quantum Crystals
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     Chapter 265 Calculation of Ensemble Averages
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     Chapter 267 Computation of Free Energy Differences
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     Chapter 269 Quantum Control
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     Chapter 270 Interior Point Methods
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     Chapter 271 Atomistic to Continuum Coupling
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     Chapter 273 Applications to Real Size Biological Systems
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     Chapter 274 Molecular Geometry Optimization: Algorithms
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     Chapter 275 Fitzhugh–Nagumo Equation
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     Chapter 276 Poisson-Nernst-Planck Equation
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     Chapter 277 Mathematical Models for Oil Reservoir Simulation
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     Chapter 279 Large-Scale Computing for Molecular Dynamics Simulation
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     Chapter 280 Convergence Acceleration
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     Chapter 281 Hierarchical Matrices
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     Chapter 282 Discontinous Galerkin Methods: Time-dependent Problems
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     Chapter 283 Computational Complexity
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     Chapter 284 Levin Quadrature
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     Chapter 285 Numerical Analysis
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     Chapter 286 Computational Dynamics
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     Chapter 287 Kinetic Equations: Computation
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     Chapter 292 Computational Partial Differential Equations
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     Chapter 293 Rational Approximation
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     Chapter 294 Bidomain Model: Computation
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     Chapter 295 Greedy Algorithms
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     Chapter 296 Preconditioning
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     Chapter 297 Eikonal Equation: Computation
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     Chapter 298 Gas Dynamics Equations: Computation
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     Chapter 299 Korteweg-de Vries Equation
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     Chapter 300 Numerical Analysis of Fredholm Integral Equations
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     Chapter 301 Machine Learning Algorithms
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     Chapter 303 Integro-Differential Equations: Computation
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     Chapter 304 Dynamic Programming
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     Chapter 306 Radial Basis Functions
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     Chapter 307 Chebyshev Iteration
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     Chapter 309 Bidomain Model: Analytical Properties
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     Chapter 312 Hardware-Oriented Numerics for PDE
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     Chapter 313 Advancing Front Methods
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     Chapter 314 Delaunay Triangulation
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     Chapter 316 Hyperbolic Conservation Laws: Analytical Properties
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     Chapter 317 Bézier Curves and Surfaces
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     Chapter 318 Numerical Steepest Descent
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     Chapter 319 Burgers Equation
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     Chapter 320 Fokker-Planck Equation: Computation
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     Chapter 321 Homotopy Methods
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     Chapter 322 Computational Proofs in Dynamics
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     Chapter 323 Multiphase Flow: Computation
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     Chapter 324 Representation of Floating-Point Numbers
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     Chapter 326 Interval Arithmetics
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     Chapter 327 Bayesian Statistics: Computation
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     Chapter 328 Metropolis Algorithms
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     Chapter 329 Interpolation
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     Chapter 330 Least Squares Finite Element Methods
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     Chapter 331 Polynomial Chaos Expansions
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     Chapter 332 Reproducibility: Methods
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     Chapter 333 Hyperbolic Conservation Laws: Computation
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     Chapter 335 Bidomain Model: Applications
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     Chapter 337 Multigrid Methods: Algebraic
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     Chapter 338 Multigrid Methods: Geometric
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     Chapter 339 Approximation of Manifold-Valued Functions
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     Chapter 340 Fisher’s Equation
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     Chapter 341 Adaptive Mesh Refinement
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     Chapter 342 Matrix Functions: Computation
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     Chapter 345 Hamilton–Jacobi Equations
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     Chapter 347 Phase Plane: Computation
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     Chapter 349 Lattice Boltzmann Methods
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     Chapter 350 hp-Version Finite Element Methods
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     Chapter 353 Conditioning
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     Chapter 354 Gabor Analysis and Algorithms
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     Chapter 355 Fast Fourier Transform
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     Chapter 357 Riemann Problem
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     Chapter 358 Least Squares Calculations
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     Chapter 359 Monte Carlo Integration
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     Chapter 360 Front Tracking
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     Chapter 362 Numerics for the Control of Partial Differential Equations
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     Chapter 364 Hodgkin-Huxley Equations
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     Chapter 365 Boundary Element Methods
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     Chapter 366 Absorbing Boundaries and Layers
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     Chapter 367 Monte Carlo Simulation
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     Chapter 370 Multivariate Approximation
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     Chapter 371 Curvelets
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     Chapter 372 Differentiation: Computation
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     Chapter 373 Inverse Problems: Numerical Methods
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     Chapter 374 Newton-Raphson Method
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     Chapter 377 Minimal Surface Equation
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     Chapter 379 Fast Marching Methods
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     Chapter 382 Diffusion Equation: Computation
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     Chapter 384 Bifurcations: Computation
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     Chapter 385 Multiresolution Methods
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     Chapter 386 Orthogonal Polynomials: Computation
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     Chapter 387 Immersed Interface/Boundary Method
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     Chapter 389 Euler Equations: Computations
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     Chapter 390 Numerical Analysis of Ordinary Differential Equations
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     Chapter 391 Quasi-Monte Carlo Methods
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     Chapter 394 Numerical Homogenization
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     Chapter 395 Filon Quadrature
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     Chapter 396 Belousov–Zhabotinsky Reaction
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     Chapter 398 Calcium Dynamics
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     Chapter 404 Bootstrapping
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     Chapter 405 Boussinesq Equations
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     Chapter 409 Discrete and Continuous Dispersion Relations
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     Chapter 411 Domain Decomposition
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     Chapter 412 Error Estimation and Adaptivity
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     Chapter 414 Finite Difference Methods
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     Chapter 415 Galerkin Methods
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     Chapter 416 Group Velocity Analysis
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     Chapter 419 Linear Programming
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     Chapter 420 Regression
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     Chapter 421 Lyapunov Exponents: Computation
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     Chapter 424 Parallel Computing
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     Chapter 425 Parallel Computing Architectures
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     Chapter 426 Parameter Identification
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     Chapter 432 Geometry Processing
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     Chapter 433 Finite Volume Methods
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     Chapter 435 ADI Methods
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     Chapter 439 Compressive Sensing
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     Chapter 445 Eigenvalues and Eigenvectors: Computation
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     Chapter 448 Fast Multipole Methods
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     Chapter 450 Finite Element Methods
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     Chapter 451 Functional Equations: Computation
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     Chapter 462 Model Reduction
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     Chapter 469 Quadratic Programming
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     Chapter 481 Electro-Mechanical Coupling in Cardiac Tissue
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     Chapter 482 Petrov-Galerkin Methods
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     Chapter 485 Linear Elastostatics
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     Chapter 487 Elastodynamics
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     Chapter 491 Composite Materials and Homogenization
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     Chapter 496 Particulate Composite Media
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     Chapter 503 Compressible Flows
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     Chapter 509 Particulate Flows (Fluid Mechanics)
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     Chapter 510 Dry Particulate Flows
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     Chapter 511 Electromagnetics-Maxwell Equations
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     Chapter 513 Medical Applications in Bone Remodeling, Wound Healing, Tumor Growth, and Cardiovascular Systems
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     Chapter 526 Methods for High-Dimensional Parametric and Stochastic Elliptic PDEs
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     Chapter 527 Analysis and Computation of Hyperbolic PDEs with Random Data
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     Chapter 531 Meshless and Meshfree Methods
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     Chapter 533 Extended Finite Element Method (XFEM)
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     Chapter 538 Global Estimates for hp-Methods
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     Chapter 546 Error Estimates for Linear Hyperbolic Equations
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     Chapter 549 A Posteriori Error Estimates of Quantities of Interest
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     Chapter 554 Discontinous Galerkin Methods: Basic Algorithms
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     Chapter 559 Direct Methods for Linear Algebraic Systems
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     Chapter 560 Multiscale Numerical Methods in Atmospheric Science
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     Chapter 562 Multiscale Multi-cloud Modeling and the Tropics
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     Chapter 563 Framework and Mathematical Strategies for Filtering or Data Assimilation
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     Chapter 567 Algorithms for Low Frequency Climate Response
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     Chapter 571 Information Theory for Climate Change and Prediction
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     Chapter 574 Dynamical Models for Climate Change
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     Chapter 575 Mathematical Methods for Large Geophysical Data Sets
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     Chapter 585 Computational Plasma Physics
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     Chapter 586 Overview of Inverse Problems