| 000 | 00371nam a2200133Ia 4500 | ||
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| 999 |
_c176806 _d176806 |
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| 020 | _a9780471115908 | ||
| 040 | _cCUS | ||
| 082 |
_a530 _bLAN/C |
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| 100 | _aLandau, Rubin H. | ||
| 245 | 0 |
_aComputational physics: problem solving with computers/ _cRubin H.Landau |
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| 260 |
_aWeinheim: _bWiley-VCH, _c1997. |
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| 300 | _axxviii,520p. | ||
| 505 | _a Parti GENERALITIES 1 Introduction 3 1.1 The Nature ofComputational Science 3 1.1.1 How Computational Scientists Do It 4 1.2 Aims of"This Book 5 1.3 Using this Book with the Disk and Web 6 2 Computing Software Basics 9 2.1 Problem 1: Making Computers Obey 9 2.2 Theory: Computer Languages 9 2.3 Implementation: Programming Concepts 11 2.4 Implementation: Fortran,area.f 12 2.5 Implementation: C,area.c 13 2.6 Implementation: Shells,Editors,and Programs 13 2.7 Theory: Program Design 14 2.8 Method: Structured Programming 16 2.9 Method: Programming Hints 18 2.10 Problem 2: Limited Range of Numbers 20 2.11 Theory: Number Representation 20 2.12 Method: Fixed and Floating 21 2.13 Implementation: Over/Underflows,over.f(.c) 23 2.14 Model: Machine Precision 23 2.15 Implementation: limit.f(.c) 24 2.16 Problem 3: Complex Numbers, Inverse Functions 25 2.17 Theory: Complex Numbers 25 2.18 Implementation: complex.c(.0 27 2.19 Exploration: Quantum Complex Energies 28 2.20 Problem 4: Summing Series 28 2.21 Method: Numeric 29 2.22 Implementation: Pseudocode 29 2.23 Implementation: Good Algorithm,exp-good.f(.c) 29 2.24 Implementation: Bad Algorithm,exp-bad.f(.c) 30 2.25 Assessment 30 $ Errors and Uncertainties in Computations 31 3.1 Problem: Living with Errors 31 3.2 Theory: Types of errors 32 3.3 Model: Subtractive Cancellation 33 3.4 Assessment: Cancellation Experiment 34 3.5 Model: Multiplicative Errors 36 3.6 Problem 1: Errors in Spherical Bessel Functions 37 3.7 Method: Numeric Recursion Relations 38 3.8 Implementation: Bessel.f(.c) 40 3.9 Assessment 40 3.10 Problem 2: Errors in Algorithms 40 3.11 Model: Errors in Algorithms 41 3.11.1 Total Error 41 3.12 Method: Optimizing with Known Error Behavior 42 3.13 Method: Empirical Error Analysis 43 3.14 Assessment: Experiment 44 Integration 47 4.1 Problem: Integrating a Spectrum 47CONTENTS fx 4.2 Model: Quadrature, Summing Boxes 47 4.3 Method: Trapezoid Rule 50 4.4 Method: Simpson's Rule 51 4.5 Assessment: Integration Error, Analytic 52 4.6 Method: Gaussian Quadrature 55 4.6.1 Scaling Integration Points 56 4.7 Implementation: integ.f(.c) 57 4.8 Assessment: Empirical Error Estimate 58 4.9 Assessment: Experimentation 59 4.10 Method: Romberg Extrapolation 59 4.10.1 Other Closed Newton-Cotes Formulas 60 Part II APPLICATIONS 5 Data Fitting 63 5.1 Problem: Fitting an Experimental Spectrum 63 5.2 Theory: Curve Fitting 64 5.3 Method: Lagrange Interpolation 65 5.3.1 Example 66 5.4 Implementation: LaGrange.f(.c) 66 5.5 Assessment: Interpolating a Resonant Spectrum 67 5.6 Assessment: Exploration 68 5.7 Method: Cubic Splines 68 5.7.1 Cubic Spline Boundary Conditions 69 5.7.2 Exploration: Cubic Spline Quadrature 70 5.8 Implementation: spline.f 71 5.9 Assessment: Spline Fit ofCross Section 71 5.10 Problem: Fitting Exponential Decay 71 5.11 Model: Exponential Decay 71 5.12 Theory: Probability Theory 73 5.13 Method: Least-Squares Fitting 74 5.14 Theory: Goodness of Fit 76 5.15 Implementation: Least-Squares Fits, fit.f(.c) 77 5.16 Assessment: Fitting Exponential Decay 78 5.17 Assessment: Fitting Heat Flow 79 5.18 Implementation: Linear Quadratic Fits 80 5.19 Assessment: Quadratic Fit 81 5.20 Method: Nonlinear Least-Squares Fitting 81* CONTENTS 5.21 Assessment: Nonlinear Fitting 82 6 Deterministic Randomness 83 6.1 Problem: Deterministic Randomness 83 6.2 Theory: Random Sequences 83 6.3 Method: Pseudo-Random-Number Generators 84 6.4 Assessment: Random Sequences 86 6.5 Implementation: Simple and Not random.f(.c); call.f(.c) 87 6.6 Assessment: Randomness and Uniformity 87 6.7 Assessment: Tests of Randomness, Uniformity 88 6.8 Problem: A Random Walk 89 6.9 Model: Random Walk Simulation 89 6.10 Method: Numerical Random Walk 90 6.11 Implementation: walk.f(.c) 91 6.12 Assessment: Different Random Walkers 91 7 Monte Carlo Applications 93 7.1 Problem: Radioactive Decay 93 7.2 Theory: Spontaneous Decay 93 7.3 Model: Discrete Decay 94 7.4 Model: Continuous Decay 95 7.5 Method: Decay Simulation 95 7.6 Implementation: decay.f(.c) 97 7.7 Assessment: Decay Visualization 97 7.8 Problem: Measuring by Stone Throwing 97 7.9 Theory: Integration by Rejection 97 7.10 Implementation: Stone Throwing,pond.f(.c) 98 7.n Problem: High-Dimensionallntegration 99 7.12 Method: Integration by Mean Value 99 7.12.1 Multidimensional Monte Carlo 101 7.13 Assessment: Error in N-D Integration 101 7.14 Implementation: 10-D Integration,int_10d.f(.c) 101 7.15 Problem: Integrate a Rapidly Varying Function© 102 7.16 Method: Variance Reduction© 102 7.17 Method: Importance Sampling© 103 7.18 Implementation: Nonuniform Randomness© 103 7.18.1 Inverse Transform Method 103 7.18.2 Uniform Weight Function w 104CONTENTS Xi 7.18.3 Exponential Weight 105 7.18.4 Gaussian(Normal)Distribution 105 7.18.5 Alternate Gaussian Distribution 106 7.19 Method: von Neumann Rejection© 107 7.20 Assessment© 108 Differentiation 109 8.1 Problem 1: Numerical Limits 109 8.2 Method: Numeric 109 8.2.1 Method: Forward Difference 109 8.2.2 Method: Central Difference 111 8.2.3 Method: Extrapolated Difference 111 8.3 Assessment: Error Analysis 112 8.4 Implementation: Differentiation,diff.f(.c) 113 8.5 Assessment: Error Analysis, Numerical 113 8.6 Problem 2: Second Derivatives 114 8.7 Theory: Newton II 114 8.8 Method: Numerical Second Derivatives 114 8.9 Assessment: Numerical Second Derivatives 115 Differential Equations and Oscillations 117 9.1 Problem: A Forced Nonlinear Oscillator 117 9.2 Theory, Physics: Newton's Laws 117 9.3 Model: Nonlinear Oscillator 118 9.4 Theory, Math: Types ofEquations 119 9.4.1 Order 119 9.4.2 Ordinary and Partial 120 9.4.3 Linear and Nonlinear 121 9.4.4 Initial and Boundary Conditions 121 9.5 Theory,^ath, and Physics: The Dynamical Form for ODEs 122 9.5.1 Second-Order Equation 122 9.6 Implementation: Dynamical Form for Oscillator 123 9.7 Numerical Method: ODE Algorithms 124 9.8 Method(Numerical): Euler's Algorithm 124 9.9 Method(Numerical): Second-Order Runge-Kutta 126 9.10 Method(Numerical): Fourth-Order Runge-Kutta 127 9.11 Implementation: ODE Solver,rk4.f(.c) 127 9.12 Assessment: rk4 and Linear Oscillations 128Xii CONTENTS 9.13 Assessment: rk4 and Nonlinear Oscillations 128 9.14 Exploration: Energy Conservation 129 10 Quantum Eigenvalues; Zero-Finding and Matching 131 10.1 Problem: Binding A Quantum Particle 131 10.2 Theory: Quantum Waves 132 10.3 Model: Particle in a Box 133 10.4 Solution: Semianalytic 133 10.5 Method: Finding Zero via Bisection Algorithm 136 10.6 Method: Eigenvalues from an ODE Solver 136 10.6.1 Matching 138 10.7 Implementation: ODE Eigenvalues,numerov.c 139 10.8 Assessment: Explorations 141 10.9 Extension: Newton's Rule for Finding Roots 141 11 Anharmonic Oscillations 143 11.1 Problem 1: Perturbed Harmonic Oscillator 143 11.2 Theory: Newton II 144 11.3 Implementation: ODE Solver,rk4.f(.c) 144 11.4 Assessment: Amplitude Dependence frequency 145 11.5 Problem 2: Realistic Pendulum 145 11.6 Theory: Newton II for Rotations 146 11.7 Method, Analytic: Elliptic Integrals 147 11.8 Implementation,rk4 for Pendulum 147 11.9 Exploration: Resonance and Beats 148 11.10 Exploration: Phase-Space Plot 149 11.11 Exploration: Damped Oscillator 150 12 Fourier Analysis of Nonlinear Oscillations 151 12.1 Problem 1: Harmonics in Nonlinear Oscillations 151 12.2 Theory: Fourier Analysis 152 12.2.1 Example 1: Sawtooth Function 154 12.2.2 Example 2: Half-Wave Function 154 12.3 Assessment: Summation of Fourier Series 155 12.4 Theory: Fourier Transforms 156 12.5 Method: Discrete Fourier Transform 157 12.6 Method: DFT for Fourier Series 161 12.7 Implementation: fourier.f(.c), in four.c 162 12.8 Assessment: Simple Analytic Input 162CONTENTS Xiii 12.9 Assessment: Highly Nonlinear Oscillator 163 12.10 Assessment: Nonlinearly Perturbed Oscillator 163 12.11 Exploration: DFT of Nonperiodic Functions 163 12.12 Exploration: Processing Noisy Signals 164 12.13 Model: Autocorrelation Function 164 12.14 Assessment: DFT and Autocorrelation Function 165 12.15 Problem 2: Model Dependence of Data Analysis © 166 12.16 Method: Model-Independent Data Analysis 167 12.17 Assessment 168 13 Unusual Dynamics of Nonlinear Systems 171 13.1 Problem: Variability of Populations 171 13.2 Theory: Nonlinear Dynamics 171 13.3 Model: Nonlinear Growth, The Logistic Map 172 13.3.1 The Logistic Map 173 13.4 Theory: Properties of Nonlinear Maps 174 13.4.1 Fixed Points 174 13.4.2 Period Doubling, Attractors 175 13.5 Implementation: Explicit Mapping 176 13.6 Assessment: Bifurcation Diagram 177 13.7 Implementation: bugs.f(.c) 178 13.8 Exploration: Random Numbers via Logistic Map 179 13.9 Exploration: Feigenbaum Constants 179 13.10 Exploration: Other Maps 180 14 Differential Chaos in Phase Space 181 14.1 Problem: A Pendulum Becomes Chaotic 181 14.2 Theory and Model: The Chaotic Pendulum 182 14.3 Theory: Limit Cycles and Mode-Locking 183 14.4 Implementation 1: Solve ODE,rk4.f(.c) 184 14.5 Visualization: Phase-Space Orbits 184 14.6 Implementation 2: Free Oscillations 187 14.7 Theory: Motion in Phase Space 188 14.8 Implementation 3: Chaotic Pendulum 188 14.9 Assessment: Chaotic Structure in Phase Space 191 14.10 Assessment: Fourier Analysis 191 14.11 Exploration: Pendulum with Vibrating Pivot 192 14.11.1 Implementation: Bifurcation Diagram 192 14.12 Further Explorations 19317 Quantum Scattering via Integral Equations© 17.1 Problem: Quantum Scattering in k Space 17.2 Theory: Lippmann-Schwinger Equation 17.3 Theory(Mathematics): Singular Integrals xlv CONTENTS Part III APPLICATIONS (HIGH PERFORMANCE COMPUTING) 15 Matrix Computing and Subroutine Libraries 197 15.1 Problem 1: Many Simultaneous Linear Equations 197 15.2 Formulation: Linear into Matrix Equation 198 15.3 Problem 2: Simple but Unsolvable Statics 198 15.4 Theory: Statics 15.5 Formulation: Nonlinear Simultaneous Equations 199 15.6 Theory: Matrix Problems 15 6.1 Classes of Matrix Problems 201 15.7 Method: Matrix Computing 15.8 Implementation: Scientific Libraries, WWW 15.9 Implementation: Determining Availability 15.9.1 Determining Contents of a Library 15.9.2 Determining the Needed Routine 15.9.3 Calling lapack from Fortran,lineq.c 15.9.4 Calling lapack from C 15.9.5 Calling lapack Fortran from C 15.9.6 C Compiling Calling Fortran 15.10 Extension: More Netlib Libraries 15.10.1 SLATEC's Common Math Library 15.11 Exercises: Testing Matrix Calls 15.12Implementation: LAPACK Short Contents 15.13 Implementation: Netlib Short Contents 15.14 Implementation: SLATEC Short Contents 6 Bound States in Momentum Space 231 16.1 Problem: Bound States in Nonlocal Potentials 16.2 Theory: k-Space Schrodinger Equation 16.3 Method: Reducing Integral to Linear Equations 233 16.4 Model: The Delta-Shell Potential 23 16.5 Implementation: Binding Energies, bound.c(.0 16.6 Exploration: Wave Function 237 | ||
| 942 | _cWB16 | ||