Holdings: Computational physics

Computational physics: with worked out examples in FORTRAN and MATLAB

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Bibliographic Details
Main Author:	Bestehorn, Michael 1957- (Author)
Format:	Book
Language:	English
Published:	Berlin ; Boston De Gruyter [2023]
Edition:	2nd edition
Series:	De Gruyter graduate
Subjects:	Computerphysik Differential Equations with Memory and Delay Differentialgleichungen mit Speicher und Verzögerung Gewöhnliche Differentialgleichungen Monte Carlo Integration Monte Carlo methods Ordinary differential equations Partial differential equations Partielle Differentialgleichungen TB: Textbook Lehrbuch
Online Access:	https://www.degruyter.com/isbn/9783110782363 Inhaltsverzeichnis
Physical Description:	XI, 396 Seiten Illustrationen, Diagramme 24 cm x 17 cm
ISBN:	9783110782363

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100	1		\|a Bestehorn, Michael \|d 1957- \|e Verfasser \|0 (DE-588)112842763 \|4 aut
245	1	0	\|a Computational physics \|b with worked out examples in FORTRAN and MATLAB \|c Michael Bestehorn
250			\|a 2nd edition
264		1	\|a Berlin ; Boston \|b De Gruyter \|c [2023]
264		4	\|c © 2023
300			\|a XI, 396 Seiten \|b Illustrationen, Diagramme \|c 24 cm x 17 cm
336			\|b txt \|2 rdacontent
337			\|b n \|2 rdamedia
338			\|b nc \|2 rdacarrier
490	0		\|a De Gruyter graduate
650	0	7	\|a Computerphysik \|0 (DE-588)4273564-6 \|2 gnd \|9 rswk-swf
653			\|a Differential Equations with Memory and Delay
653			\|a Differentialgleichungen mit Speicher und Verzögerung
653			\|a Gewöhnliche Differentialgleichungen
653			\|a Monte Carlo Integration
653			\|a Monte Carlo methods
653			\|a Ordinary differential equations
653			\|a Partial differential equations
653			\|a Partielle Differentialgleichungen
653			\|a TB: Textbook
655		7	\|0 (DE-588)4123623-3 \|a Lehrbuch \|2 gnd-content
689	0	0	\|a Computerphysik \|0 (DE-588)4273564-6 \|D s
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999			\|a oai:aleph.bib-bvb.de:BVB01-034199723

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_version_	1804185131975442432
adam_text	CONTENTS 1 INTRODUCTION - 1 1.1 GOAL, CONTENTS, AND OUTLINE - 1 1.2 THE ENVIRONMENT REQUIRED FOR PROGRAM DEVELOPMENT - 5 1.2.1 OPERATING SYSTEM - 5 1.2.2 SOFTWARE PACKAGES - 6 1.2.3 GRAPHICS - 6 1.2.4 PROGRAM DEVELOPMENT AND A SIMPLE SCRIPT - 6 1.3 A FIRST EXAMPLE - THE LOGISTIC MAP - 7 1.3.1 MAP - 7 1.3.2 FORTRAN ---- 9 1.3.3 PROBLEMS - 12 BIBLIOGRAPHY - 12 2 NONLINEAR MAPS - 13 2.1 FRENKEL-KOTOROVA MODEL - 13 2.1.1 CLASSICAL FORMULATION - 13 2.1.2 EQUILIBRIUM SOLUTIONS - 14 2.1.3 THE STANDARD MAP - 14 2.1.4 PROBLEMS - 15 2.2 CHAOS AND LYAPUNOV EXPONENTS - 16 2.2.1 STABILITY, BUTTERFLY EFFECT, AND CHAOS - 16 2.2.2 LYAPUNOV EXPONENT OF THE LOGISTIC MAP - 17 2.2.3 LYAPUNOV EXPONENTS FOR MULTIDIMENSIONAL MAPS - 19 2.3 AFFINE MAPS AND FRACTALS - 22 2.3.1 SIERPINSKI TRIANGLE - 23 2.3.2 ABOUT FERNS AND OTHER PLANTS - 25 2.3.3 PROBLEMS - 26 2.4 FRACTAL DIMENSION - 26 2.4.1 BOX-COUNTING - 26 2.4.2 APPLICATION: SIERPINSKI TRIANGLE - 27 2.4.3 PROBLEM - 28 2.5 NEURAL NETWORKS - 29 2.5.1 PERCEPTRON - 29 2.5.2 SELF-ORGANIZED MAPS: KOHONEN S MODEL - 36 2.5.3 PROBLEMS - 40 BIBLIOGRAPHY - 40 3 DYNAMICAL SYSTEMS - 42 3.1 QUASILINEAR DIFFERENTIAL EQUATIONS - 42 3.1.1 EXAMPLE: LOGISTIC MAP AND LOGISTIC ODE - 44 VI - CONTENTS 3.1.2 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7 3.3 3.3.1 3.3.2 3.3.3 PROBLEMS - 45 FIXED POINTS AND INSTABILITIES - 45 FIXED POINTS - 45 STABILITY - 45 TRAJECTORIES - 47 GRADIENT DYNAMICS - 47 SPECIAL CASE N = 1 - 48 SPECIAL CASE N = 2 - 48 SPECIAL CASE N = 3 - 50 HAMILTONIAN SYSTEMS - 53 HAMILTON FUNCTION AND CANONICAL EQUATIONS - 53 SYMPLECTIC INTEGRATORS - 54 POINCARE SECTION - 60 BIBLIOGRAPHY - 62 4 4.1 4.1.1 4.1.2 4.2 4.2.1 4.2.2 4.2.3 4.3 4.3.1 4.3.2 4.3.3 4.4 4.4.1 4.4.2 4.4.3 4.4.4 4.4.5 4.5 4.5.1 4.5.2 4.5.3 4.5.4 4.5.5 4.5.6 4.6 4.6.1 ORDINARY DIFFERENTIAL EQUATIONS I, INITIAL VALUE PROBLEMS - 63 NEWTON S MECHANICS - 63 EQUATIONS OF MOTION - 63 THE MATHEMATICAL PENDULUM - 64 NUMERICAL METHODS OF THE LOWEST ORDER - 65 EULER METHOD - 65 NUMERICAL STABILITY OF THE EULER METHOD - 67 IMPLICIT AND EXPLICIT METHODS - 68 HIGHER ORDER METHODS - 69 HEUN S METHOD - 70 PROBLEMS - 73 RUNGE-KUTTA METHOD - 73 RK4 APPLICATIONS: CELESTIAL MECHANICS - 79 KEPLER PROBLEM: CLOSED ORBITS - 79 QUASIPERIODIC ORBITS AND APSIDAL PRECESSION - 82 MULTIPLE PLANETS: IS OUR SOLAR SYSTEM STABLE? - 83 THE REDUCED THREE-BODY PROBLEM - 86 PROBLEMS - 92 MOLECULAR DYNAMICS (MD) - 93 CLASSICAL FORMULATION - 93 BOUNDARY CONDITIONS - 94 MICROCANONICAL AND CANONICAL ENSEMBLE - 95 A SYMPLECTIC ALGORITHM - 96 EVALUATION - 97 PROBLEMS - 101 CHAOS - 102 HARMONICALLY DRIVEN PENDULUM - 103 CONTENTS - VII 4.6.2 4.6.3 4.6.4 4.6.5 4.7 4.7.1 4.7.2 4.7.3 4.7.4 4.7.5 POINCARE SECTION AND BIFURCATION DIAGRAMS - 105 LYAPUNOV EXPONENTS - 105 FRACTAL DIMENSION - 115 RECONSTRUCTION OF ATTRACTORS - 117 DIFFERENTIAL EQUATIONS WITH PERIODIC COEFFICIENTS - 119 FLOQUET THEOREM - 119 STABILITY OF LIMIT CYCLES - 121 PARAMETRIC INSTABILITY: PENDULUM WITH AN OSCILLATING SUPPORT - 121 MATHIEU EQUATION - 123 PROBLEMS - 125 BIBLIOGRAPHY - 125 5 5.1 5.1.1 5.1.2 5.2 5.2.1 5.2.2 5.3 5.3.1 5.3.2 5.4 5.4.1 5.4.2 5.4.3 5.4.4 5.5 5.5.1 5.5.2 5.5.3 5.6 ORDINARY DIFFERENTIAL EQUATIONS II, BOUNDARY VALUE PROBLEMS - 127 PRELIMINARY REMARKS - 127 BOUNDARY CONDITIONS - 127 EXAMPLE: BALLISTIC FLIGHT - 128 FINITE DIFFERENCES - 129 DISCRETIZATION - 129 EXAMPLE: SCHRODINGER EQUATION - 132 WEIGHTED RESIDUAL METHODS - 138 WEIGHT AND BASE FUNCTIONS - 138 EXAMPLE: STARK EFFECT - 140 NONLINEAR BOUNDARY VALUE PROBLEMS - 142 NONLINEAR SYSTEMS - 143 NEWTON-RAPHSON - 144 EXAMPLE: THE NONLINEAR SCHRODINGER EQUATION - 145 EXAMPLE: A MOONSHOT - 148 SHOOTING - 151 THE METHOD - 151 EXAMPLE: FREE FALL WITH QUADRATIC FRICTION - 152 SYSTEMS OF EQUATIONS - 154 PROBLEMS - 155 BIBLIOGRAPHY - 155 6 6.1 6.1.1 6.1.2 6.1.3 6.2 6.2.1 6.2.2 ORDINARY DIFFERENTIAL EQUATIONS III, MEMORY, DELAY AND NOISE - 156 WHY MEMORY? TWO EXAMPLES AND NUMERICAL METHODS - 156 LOGISTIC EQUATION - THE HUTCHINSON-WRIGHT EQUATION - 157 POINTER METHOD - 159 MACKEY-GLASS EQUATION - 160 LINEARIZED MEMORY EQUATIONS AND OSCILLATORY INSTABILITY - 163 STABILITY OF A FIXED POINT - 163 ONE EQUATION, ONE 8-KERNEL - 164 VIII - CONTENTS 6.2.3 6.3 6.3.1 6.3.2 6.3.3 6.3.4 6.4 6.4.1 6.4.2 6.4.3 6.4.4 6.4.5 6.5 6.5.1 6.5.2 6.5.3 6.5.4 6.6 6.6.1 6.6.2 6.6.3 6.6.4 ONE EQUATION, ONE ARBITRARY KERNEL - 169 CHAOS AND LYAPUNOV EXPONENTS FOR MEMORY SYSTEMS - 171 PROJECTION ONTO A FINITE DIMENSIONAL SYSTEM OF ODES - 171 DETERMINATION OF THE LARGEST LYAPUNOV EXPONENT - 171 THE COMPLETE LYAPUNOV SPECTRUM - 173 PROBLEMS - 174 EPIDEMIC MODELS - 175 PREDATOR-PREY SYSTEMS AND SIR MODEL - 175 SIRS MODEL - 180 SIRS MODEL WITH INFECTION RATE CONTROL - 183 DELAYED INFECTION RATE CONTROL - 183 PROBLEMS - 186 NOISE AND STOCHASTIC DIFFERENTIAL EQUATIONS - 186 BROWNIAN MOTION - 186 STOCHASTIC DIFFERENTIAL EQUATION - 189 STOCHASTIC DELAY DIFFERENTIAL EQUATION - 191 SIRS MODEL WITH DELAYED AND NOISY INFECTION RATE CONTROL - 191 A MICROSCOPIC TRAFFIC FLOW MODEL - 194 THE MODEL - 194 THE NONDIMENSIONAL BASIC SYSTEM - 196 STATIONARY SOLUTION AND LINEAR STABILITY ANALYSIS - 196 THE FULLY NONLINEAR SYSTEM - NUMERICAL SOLUTIONS - 199 BIBLIOGRAPHY - 201 7 7.1 7.1.1 7.1.2 7.1.3 7.2 7.2.1 7.2.2 7.2.3 7.2.4 7.3 7.3.1 7.3.2 7.3.3 7.4 7.4.1 7.4.2 7.4.3 PARTIAL DIFFERENTIAL EQUATIONS I, BASICS - 202 CLASSIFICATION - 202 PDES OF THE FIRST ORDER - 202 PDES OF THE SECOND ORDER - 205 BOUNDARY AND INITIAL CONDITIONS - 207 FINITE DIFFERENCES - 211 DISCRETIZATION - 211 ELLIPTIC PDES, EXAMPLE: POISSON EQUATION - 214 PARABOLIC PDES, EXAMPLE: HEAT EQUATION - 220 HYPERBOLIC PDES, EXAMPLE: CONVECTION EQUATION, WAVE EQUATION - 226 ALTERNATIVE DISCRETIZATION METHODS - 232 CHEBYSHEV SPECTRAL METHOD - 233 SPECTRAL METHOD BY FOURIER TRANSFORMATION - 238 FINITE-ELEMENT METHOD - 242 NONLINEAR PDES - 246 REAL GINZBURG-LANDAU EQUATION - 247 NUMERICAL SOLUTION, EXPLICIT METHOD - 248 NUMERICAL SOLUTION, SEMI-IMPLICIT METHOD - 249 CONTENTS - IX 7.4.4 PROBLEMS - 251 BIBLIOGRAPHY - 253 8 PARTIAL DIFFERENTIAL EQUATIONS II, APPLICATIONS - 254 8.1 QUANTUM MECHANICS IN ONE DIMENSION - 254 8.1.1 STATIONARY TWO-PARTICLE EQUATION - 254 8.1.2 TIME-DEPENDENT SCHRODINGER EQUATION - 257 8.2 QUANTUM MECHANICS IN TWO DIMENSIONS - 263 8.2.1 SCHRODINGER EQUATION - 264 8.2.2 ALGORITHM - 264 8.2.3 EVALUATION - 265 8.3 FLUID MECHANICS: FLOW OF AN INCOMPRESSIBLE LIQUID - 266 8.3.1 HYDRODYNAMIC BASIC EQUATIONS - 266 8.3.2 EXAMPLE: DRIVEN CAVITY - 269 8.3.3 THERMAL CONVECTION: (A) SQUARE GEOMETRY - 272 8.3.4 THERMAL CONVECTION: (B) RAYLEIGH-BENARD CONVECTION - 281 8.4 PATTERN FORMATION OUT OF EQUILIBRIUM - 289 8.4.1 REACTION-DIFFUSION SYSTEMS - 289 8.4.2 SWIFT-HOHENBERG EQUATION - 298 8.4.3 PROBLEMS - 303 BIBLIOGRAPHY - 304 9 MONTE CARLO METHODS - 305 9.1 RANDOM NUMBERS AND DISTRIBUTIONS - 305 9.1.1 RANDOM NUMBER GENERATOR - 305 9.1.2 DISTRIBUTION FUNCTION, PROBABILITY DENSITY, MEAN VALUES - 306 9.1.3 OTHER DISTRIBUTION FUNCTIONS - 307 9.2 MONTE CARLO INTEGRATION - 311 9.2.1 INTEGRALS IN ONE DIMENSION - 311 9.2.2 INTEGRALS IN HIGHER DIMENSIONS - 313 9.3 APPLICATIONS FROM STATISTICAL PHYSICS - 315 9.3.1 TWO-DIMENSIONAL CLASSICAL GAS - 316 9.3.2 THE ISING MODEL - 322 9.4 DIFFERENTIAL EQUATIONS DERIVED FROM VARIATIONAL PROBLEMS - 332 9.4.1 DIFFUSION EQUATION - 332 9.4.2 SWIFT-HOHENBERG EQUATION - 334 BIBLIOGRAPHY - 335 A MATRICES AND SYSTEMS OF LINEAR EQUATIONS - 337 A.1 REAL-VALUED MATRICES - 337 A.1.1 EIGENVALUES AND EIGENVECTORS - 337 A.1.2 CHARACTERISTIC POLYNOMIAL - 337 X - CONTENTS A.1. 3 A.1 .4 A.2 A.2.1 A.2.2 A.3 A.3.1 A.3.2 A.3.3 A.3.4 A.3.5 A.4 A.4.1 A.4.2 A.4.3 NOTATIONS - 338 NORMAL MATRICES - 338 COMPLEX-VALUED MATRICES - 339 NOTATIONS - 339 JORDAN CANONICAL FORM - 340 INHOMOGENEOUS SYSTEMS OF LINEAR EQUATIONS - 341 REGULAR AND SINGULAR SYSTEM MATRICES - 341 FREDHOLM ALTERNATIVE - 342 REGULAR MATRICES - 343 LU DECOMPOSITION - 343 THOMAS ALGORITHM - 346 HOMOGENEOUS SYSTEMS OF LINEAR EQUATIONS - 347 EIGENVALUE PROBLEMS - 347 DIAGONALIZATION - 347 APPLICATION: ZEROS OF A POLYNOMIAL - 350 BIBLIOGRAPHY - 351 B B.1 B.2 B.2.1 B.2.2 B.2.3 B.2.4 B.2.5 B.2.6 B.3 B.3.1 B.3.2 B.3.3 B.3.4 B.4 B.4.1 B.4.2 B.4.3 B.4.4 B.4.5 B.4.6 B.4.7 B.4.8 B.4.9 PROGRAM LIBRARY - 353 ROUTINES - 353 GRAPHICS - 354 INIT - 354 CONTUR - 354 CONTURL - 354 CCONTU - 355 IMAGE - 355 CCIRCL - 355 RUNGE-KUTTA - 355 RKG - 355 DRKG - 356 DRKADT - 356 RKG_DEL - 356 MISCELLANEOUS - 356 TRIDAG - THOMAS ALGORITHM - 356 CTRIDA - 357 DLYAP_EXP - LYAPUNOV EXPONENTS - 357 DLYAP_DEL - LARGEST LYAPUNOV EXPONENT OF DELAY-SYSTEM - 357 DLYAP_EXP_DEL - LYAPUNOV EXPONENTS OF DELAY-SYSTEM - 358 SCHMID - ORTHOGONALIZATION - 358 FUNCTION VOLUM - VOLUME IN N DIMENSIONS - 359 FUNCTION DETER - DETERMINANT - 359 RANDOM_INIT - RANDOM NUMBERS - 359 CONTENTS - XI INDEX - 393 C C.1 C.2 C.3 C.4 C.5 C.6 C.7 C.8 SOLUTIONS OF THE PROBLEMS - 361 CHAPTER 1 - 361 CHAPTER 2 - 362 CHAPTER 3 - 362 CHAPTER 4 - 364 CHAPTER 5 - 374 CHAPTER 6 - 376 CHAPTER? - 378 CHAPTERS - 382 D D.1 D.2 D.2.1 D.2.2 D.2.3 README AND A SHORT GUIDE TO FE-TOOLS - 387 README -----387 SHORT GUIDE TO FINITE-ELEMENT TOOLS FROM CHAPTER 7 - 390 MESH_GENERATOR - 390 LAPLACE_SOLVER - 391 GRID_CONTUR - 392
adam_txt	CONTENTS 1 INTRODUCTION - 1 1.1 GOAL, CONTENTS, AND OUTLINE - 1 1.2 THE ENVIRONMENT REQUIRED FOR PROGRAM DEVELOPMENT - 5 1.2.1 OPERATING SYSTEM - 5 1.2.2 SOFTWARE PACKAGES - 6 1.2.3 GRAPHICS - 6 1.2.4 PROGRAM DEVELOPMENT AND A SIMPLE SCRIPT - 6 1.3 A FIRST EXAMPLE - THE LOGISTIC MAP - 7 1.3.1 MAP - 7 1.3.2 FORTRAN ---- 9 1.3.3 PROBLEMS - 12 BIBLIOGRAPHY - 12 2 NONLINEAR MAPS - 13 2.1 FRENKEL-KOTOROVA MODEL - 13 2.1.1 CLASSICAL FORMULATION - 13 2.1.2 EQUILIBRIUM SOLUTIONS - 14 2.1.3 THE STANDARD MAP - 14 2.1.4 PROBLEMS - 15 2.2 CHAOS AND LYAPUNOV EXPONENTS - 16 2.2.1 STABILITY, BUTTERFLY EFFECT, AND CHAOS - 16 2.2.2 LYAPUNOV EXPONENT OF THE LOGISTIC MAP - 17 2.2.3 LYAPUNOV EXPONENTS FOR MULTIDIMENSIONAL MAPS - 19 2.3 AFFINE MAPS AND FRACTALS - 22 2.3.1 SIERPINSKI TRIANGLE - 23 2.3.2 ABOUT FERNS AND OTHER PLANTS - 25 2.3.3 PROBLEMS - 26 2.4 FRACTAL DIMENSION - 26 2.4.1 BOX-COUNTING - 26 2.4.2 APPLICATION: SIERPINSKI TRIANGLE - 27 2.4.3 PROBLEM - 28 2.5 NEURAL NETWORKS - 29 2.5.1 PERCEPTRON - 29 2.5.2 SELF-ORGANIZED MAPS: KOHONEN ' S MODEL - 36 2.5.3 PROBLEMS - 40 BIBLIOGRAPHY - 40 3 DYNAMICAL SYSTEMS - 42 3.1 QUASILINEAR DIFFERENTIAL EQUATIONS - 42 3.1.1 EXAMPLE: LOGISTIC MAP AND LOGISTIC ODE - 44 VI - CONTENTS 3.1.2 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7 3.3 3.3.1 3.3.2 3.3.3 PROBLEMS - 45 FIXED POINTS AND INSTABILITIES - 45 FIXED POINTS - 45 STABILITY - 45 TRAJECTORIES - 47 GRADIENT DYNAMICS - 47 SPECIAL CASE N = 1 - 48 SPECIAL CASE N = 2 - 48 SPECIAL CASE N = 3 - 50 HAMILTONIAN SYSTEMS - 53 HAMILTON FUNCTION AND CANONICAL EQUATIONS - 53 SYMPLECTIC INTEGRATORS - 54 POINCARE SECTION - 60 BIBLIOGRAPHY - 62 4 4.1 4.1.1 4.1.2 4.2 4.2.1 4.2.2 4.2.3 4.3 4.3.1 4.3.2 4.3.3 4.4 4.4.1 4.4.2 4.4.3 4.4.4 4.4.5 4.5 4.5.1 4.5.2 4.5.3 4.5.4 4.5.5 4.5.6 4.6 4.6.1 ORDINARY DIFFERENTIAL EQUATIONS I, INITIAL VALUE PROBLEMS - 63 NEWTON ' S MECHANICS - 63 EQUATIONS OF MOTION - 63 THE MATHEMATICAL PENDULUM - 64 NUMERICAL METHODS OF THE LOWEST ORDER - 65 EULER METHOD - 65 NUMERICAL STABILITY OF THE EULER METHOD - 67 IMPLICIT AND EXPLICIT METHODS - 68 HIGHER ORDER METHODS - 69 HEUN ' S METHOD - 70 PROBLEMS - 73 RUNGE-KUTTA METHOD - 73 RK4 APPLICATIONS: CELESTIAL MECHANICS - 79 KEPLER PROBLEM: CLOSED ORBITS - 79 QUASIPERIODIC ORBITS AND APSIDAL PRECESSION - 82 MULTIPLE PLANETS: IS OUR SOLAR SYSTEM STABLE? - 83 THE REDUCED THREE-BODY PROBLEM - 86 PROBLEMS - 92 MOLECULAR DYNAMICS (MD) - 93 CLASSICAL FORMULATION - 93 BOUNDARY CONDITIONS - 94 MICROCANONICAL AND CANONICAL ENSEMBLE - 95 A SYMPLECTIC ALGORITHM - 96 EVALUATION - 97 PROBLEMS - 101 CHAOS - 102 HARMONICALLY DRIVEN PENDULUM - 103 CONTENTS - VII 4.6.2 4.6.3 4.6.4 4.6.5 4.7 4.7.1 4.7.2 4.7.3 4.7.4 4.7.5 POINCARE SECTION AND BIFURCATION DIAGRAMS - 105 LYAPUNOV EXPONENTS - 105 FRACTAL DIMENSION - 115 RECONSTRUCTION OF ATTRACTORS - 117 DIFFERENTIAL EQUATIONS WITH PERIODIC COEFFICIENTS - 119 FLOQUET THEOREM - 119 STABILITY OF LIMIT CYCLES - 121 PARAMETRIC INSTABILITY: PENDULUM WITH AN OSCILLATING SUPPORT - 121 MATHIEU EQUATION - 123 PROBLEMS - 125 BIBLIOGRAPHY - 125 5 5.1 5.1.1 5.1.2 5.2 5.2.1 5.2.2 5.3 5.3.1 5.3.2 5.4 5.4.1 5.4.2 5.4.3 5.4.4 5.5 5.5.1 5.5.2 5.5.3 5.6 ORDINARY DIFFERENTIAL EQUATIONS II, BOUNDARY VALUE PROBLEMS - 127 PRELIMINARY REMARKS - 127 BOUNDARY CONDITIONS - 127 EXAMPLE: BALLISTIC FLIGHT - 128 FINITE DIFFERENCES - 129 DISCRETIZATION - 129 EXAMPLE: SCHRODINGER EQUATION - 132 WEIGHTED RESIDUAL METHODS - 138 WEIGHT AND BASE FUNCTIONS - 138 EXAMPLE: STARK EFFECT - 140 NONLINEAR BOUNDARY VALUE PROBLEMS - 142 NONLINEAR SYSTEMS - 143 NEWTON-RAPHSON - 144 EXAMPLE: THE NONLINEAR SCHRODINGER EQUATION - 145 EXAMPLE: A MOONSHOT - 148 SHOOTING - 151 THE METHOD - 151 EXAMPLE: FREE FALL WITH QUADRATIC FRICTION - 152 SYSTEMS OF EQUATIONS - 154 PROBLEMS - 155 BIBLIOGRAPHY - 155 6 6.1 6.1.1 6.1.2 6.1.3 6.2 6.2.1 6.2.2 ORDINARY DIFFERENTIAL EQUATIONS III, MEMORY, DELAY AND NOISE - 156 WHY MEMORY? TWO EXAMPLES AND NUMERICAL METHODS - 156 LOGISTIC EQUATION - THE HUTCHINSON-WRIGHT EQUATION - 157 POINTER METHOD - 159 MACKEY-GLASS EQUATION - 160 LINEARIZED MEMORY EQUATIONS AND OSCILLATORY INSTABILITY - 163 STABILITY OF A FIXED POINT - 163 ONE EQUATION, ONE 8-KERNEL - 164 VIII - CONTENTS 6.2.3 6.3 6.3.1 6.3.2 6.3.3 6.3.4 6.4 6.4.1 6.4.2 6.4.3 6.4.4 6.4.5 6.5 6.5.1 6.5.2 6.5.3 6.5.4 6.6 6.6.1 6.6.2 6.6.3 6.6.4 ONE EQUATION, ONE ARBITRARY KERNEL - 169 CHAOS AND LYAPUNOV EXPONENTS FOR MEMORY SYSTEMS - 171 PROJECTION ONTO A FINITE DIMENSIONAL SYSTEM OF ODES - 171 DETERMINATION OF THE LARGEST LYAPUNOV EXPONENT - 171 THE COMPLETE LYAPUNOV SPECTRUM - 173 PROBLEMS - 174 EPIDEMIC MODELS - 175 PREDATOR-PREY SYSTEMS AND SIR MODEL - 175 SIRS MODEL - 180 SIRS MODEL WITH INFECTION RATE CONTROL - 183 DELAYED INFECTION RATE CONTROL - 183 PROBLEMS - 186 NOISE AND STOCHASTIC DIFFERENTIAL EQUATIONS - 186 BROWNIAN MOTION - 186 STOCHASTIC DIFFERENTIAL EQUATION - 189 STOCHASTIC DELAY DIFFERENTIAL EQUATION - 191 SIRS MODEL WITH DELAYED AND NOISY INFECTION RATE CONTROL - 191 A MICROSCOPIC TRAFFIC FLOW MODEL - 194 THE MODEL - 194 THE NONDIMENSIONAL BASIC SYSTEM - 196 STATIONARY SOLUTION AND LINEAR STABILITY ANALYSIS - 196 THE FULLY NONLINEAR SYSTEM - NUMERICAL SOLUTIONS - 199 BIBLIOGRAPHY - 201 7 7.1 7.1.1 7.1.2 7.1.3 7.2 7.2.1 7.2.2 7.2.3 7.2.4 7.3 7.3.1 7.3.2 7.3.3 7.4 7.4.1 7.4.2 7.4.3 PARTIAL DIFFERENTIAL EQUATIONS I, BASICS - 202 CLASSIFICATION - 202 PDES OF THE FIRST ORDER - 202 PDES OF THE SECOND ORDER - 205 BOUNDARY AND INITIAL CONDITIONS - 207 FINITE DIFFERENCES - 211 DISCRETIZATION - 211 ELLIPTIC PDES, EXAMPLE: POISSON EQUATION - 214 PARABOLIC PDES, EXAMPLE: HEAT EQUATION - 220 HYPERBOLIC PDES, EXAMPLE: CONVECTION EQUATION, WAVE EQUATION - 226 ALTERNATIVE DISCRETIZATION METHODS - 232 CHEBYSHEV SPECTRAL METHOD - 233 SPECTRAL METHOD BY FOURIER TRANSFORMATION - 238 FINITE-ELEMENT METHOD - 242 NONLINEAR PDES - 246 REAL GINZBURG-LANDAU EQUATION - 247 NUMERICAL SOLUTION, EXPLICIT METHOD - 248 NUMERICAL SOLUTION, SEMI-IMPLICIT METHOD - 249 CONTENTS - IX 7.4.4 PROBLEMS - 251 BIBLIOGRAPHY - 253 8 PARTIAL DIFFERENTIAL EQUATIONS II, APPLICATIONS - 254 8.1 QUANTUM MECHANICS IN ONE DIMENSION - 254 8.1.1 STATIONARY TWO-PARTICLE EQUATION - 254 8.1.2 TIME-DEPENDENT SCHRODINGER EQUATION - 257 8.2 QUANTUM MECHANICS IN TWO DIMENSIONS - 263 8.2.1 SCHRODINGER EQUATION - 264 8.2.2 ALGORITHM - 264 8.2.3 EVALUATION - 265 8.3 FLUID MECHANICS: FLOW OF AN INCOMPRESSIBLE LIQUID - 266 8.3.1 HYDRODYNAMIC BASIC EQUATIONS - 266 8.3.2 EXAMPLE: DRIVEN CAVITY - 269 8.3.3 THERMAL CONVECTION: (A) SQUARE GEOMETRY - 272 8.3.4 THERMAL CONVECTION: (B) RAYLEIGH-BENARD CONVECTION - 281 8.4 PATTERN FORMATION OUT OF EQUILIBRIUM - 289 8.4.1 REACTION-DIFFUSION SYSTEMS - 289 8.4.2 SWIFT-HOHENBERG EQUATION - 298 8.4.3 PROBLEMS - 303 BIBLIOGRAPHY - 304 9 MONTE CARLO METHODS - 305 9.1 RANDOM NUMBERS AND DISTRIBUTIONS - 305 9.1.1 RANDOM NUMBER GENERATOR - 305 9.1.2 DISTRIBUTION FUNCTION, PROBABILITY DENSITY, MEAN VALUES - 306 9.1.3 OTHER DISTRIBUTION FUNCTIONS - 307 9.2 MONTE CARLO INTEGRATION - 311 9.2.1 INTEGRALS IN ONE DIMENSION - 311 9.2.2 INTEGRALS IN HIGHER DIMENSIONS - 313 9.3 APPLICATIONS FROM STATISTICAL PHYSICS - 315 9.3.1 TWO-DIMENSIONAL CLASSICAL GAS - 316 9.3.2 THE ISING MODEL - 322 9.4 DIFFERENTIAL EQUATIONS DERIVED FROM VARIATIONAL PROBLEMS - 332 9.4.1 DIFFUSION EQUATION - 332 9.4.2 SWIFT-HOHENBERG EQUATION - 334 BIBLIOGRAPHY - 335 A MATRICES AND SYSTEMS OF LINEAR EQUATIONS - 337 A.1 REAL-VALUED MATRICES - 337 A.1.1 EIGENVALUES AND EIGENVECTORS - 337 A.1.2 CHARACTERISTIC POLYNOMIAL - 337 X - CONTENTS A.1. 3 A.1 .4 A.2 A.2.1 A.2.2 A.3 A.3.1 A.3.2 A.3.3 A.3.4 A.3.5 A.4 A.4.1 A.4.2 A.4.3 NOTATIONS - 338 NORMAL MATRICES - 338 COMPLEX-VALUED MATRICES - 339 NOTATIONS - 339 JORDAN CANONICAL FORM - 340 INHOMOGENEOUS SYSTEMS OF LINEAR EQUATIONS - 341 REGULAR AND SINGULAR SYSTEM MATRICES - 341 FREDHOLM ALTERNATIVE - 342 REGULAR MATRICES - 343 LU DECOMPOSITION - 343 THOMAS ALGORITHM - 346 HOMOGENEOUS SYSTEMS OF LINEAR EQUATIONS - 347 EIGENVALUE PROBLEMS - 347 DIAGONALIZATION - 347 APPLICATION: ZEROS OF A POLYNOMIAL - 350 BIBLIOGRAPHY - 351 B B.1 B.2 B.2.1 B.2.2 B.2.3 B.2.4 B.2.5 B.2.6 B.3 B.3.1 B.3.2 B.3.3 B.3.4 B.4 B.4.1 B.4.2 B.4.3 B.4.4 B.4.5 B.4.6 B.4.7 B.4.8 B.4.9 PROGRAM LIBRARY - 353 ROUTINES - 353 GRAPHICS - 354 INIT - 354 CONTUR - 354 CONTURL - 354 CCONTU - 355 IMAGE - 355 CCIRCL - 355 RUNGE-KUTTA - 355 RKG - 355 DRKG - 356 DRKADT - 356 RKG_DEL - 356 MISCELLANEOUS - 356 TRIDAG - THOMAS ALGORITHM - 356 CTRIDA - 357 DLYAP_EXP - LYAPUNOV EXPONENTS - 357 DLYAP_DEL - LARGEST LYAPUNOV EXPONENT OF DELAY-SYSTEM - 357 DLYAP_EXP_DEL - LYAPUNOV EXPONENTS OF DELAY-SYSTEM - 358 SCHMID - ORTHOGONALIZATION - 358 FUNCTION VOLUM - VOLUME IN N DIMENSIONS - 359 FUNCTION DETER - DETERMINANT - 359 RANDOM_INIT - RANDOM NUMBERS - 359 CONTENTS - XI INDEX - 393 C C.1 C.2 C.3 C.4 C.5 C.6 C.7 C.8 SOLUTIONS OF THE PROBLEMS - 361 CHAPTER 1 - 361 CHAPTER 2 - 362 CHAPTER 3 - 362 CHAPTER 4 - 364 CHAPTER 5 - 374 CHAPTER 6 - 376 CHAPTER? - 378 CHAPTERS - 382 D D.1 D.2 D.2.1 D.2.2 D.2.3 README AND A SHORT GUIDE TO FE-TOOLS - 387 README -----387 SHORT GUIDE TO FINITE-ELEMENT TOOLS FROM CHAPTER 7 - 390 MESH_GENERATOR - 390 LAPLACE_SOLVER - 391 GRID_CONTUR - 392
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spelling	Bestehorn, Michael 1957- Verfasser (DE-588)112842763 aut Computational physics with worked out examples in FORTRAN and MATLAB Michael Bestehorn 2nd edition Berlin ; Boston De Gruyter [2023] © 2023 XI, 396 Seiten Illustrationen, Diagramme 24 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter graduate Computerphysik (DE-588)4273564-6 gnd rswk-swf Differential Equations with Memory and Delay Differentialgleichungen mit Speicher und Verzögerung Gewöhnliche Differentialgleichungen Monte Carlo Integration Monte Carlo methods Ordinary differential equations Partial differential equations Partielle Differentialgleichungen TB: Textbook (DE-588)4123623-3 Lehrbuch gnd-content Computerphysik (DE-588)4273564-6 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-078252-3 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-078266-0 X:MVB https://www.degruyter.com/isbn/9783110782363 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034199723&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Bestehorn, Michael 1957- Computational physics with worked out examples in FORTRAN and MATLAB Computerphysik (DE-588)4273564-6 gnd
subject_GND	(DE-588)4273564-6 (DE-588)4123623-3
title	Computational physics with worked out examples in FORTRAN and MATLAB
title_auth	Computational physics with worked out examples in FORTRAN and MATLAB
title_exact_search	Computational physics with worked out examples in FORTRAN and MATLAB
title_exact_search_txtP	Computational physics with worked out examples in FORTRAN and MATLAB
title_full	Computational physics with worked out examples in FORTRAN and MATLAB Michael Bestehorn
title_fullStr	Computational physics with worked out examples in FORTRAN and MATLAB Michael Bestehorn
title_full_unstemmed	Computational physics with worked out examples in FORTRAN and MATLAB Michael Bestehorn
title_short	Computational physics
title_sort	computational physics with worked out examples in fortran and matlab
title_sub	with worked out examples in FORTRAN and MATLAB
topic	Computerphysik (DE-588)4273564-6 gnd
topic_facet	Computerphysik Lehrbuch
url	https://www.degruyter.com/isbn/9783110782363 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034199723&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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