MATLAB Mathematics - SERC - Index of

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Introduction to Initial Value ODE Problems . . . . . . . . . . . . . . . 5-4 Solvers for Explicit and Linearly Implicit ODEs . . . . . . . . . . . . 5-5 Examples: Solving Explicit ODE Problems . . . . . . . . . . . . . . . . 5-9 Solver for Fully Implicit ODEs . . . . . . . . . . . . . . . . . . . . . . . . . 5-15 Example: Solving a Fully Implicit ODE Problem . . . . . . . . . . 5-16 Changing ODE Integration Properties . . . . . . . . . . . . . . . . . . . 5-17 Examples: Applying the ODE Initial Value Problem Solvers . 5-18 Questions and Answers, and Troubleshooting . . . . . . . . . . . . . 5-43 Initial Value Problems for DDEs . . . . . . . . . . . . . . . . . . . . . . . 5-49 DDE Function Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-49 Introduction to Initial Value DDE Problems . . . . . . . . . . . . . . 5-50 DDE Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-51 Solving DDE Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-53 Discontinuities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-57 Changing DDE Integration Properties . . . . . . . . . . . . . . . . . . . 5-60 Boundary Value Problems for ODEs . . . . . . . . . . . . . . . . . . . 5-61 BVP Function Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-62 Introduction to Boundary Value ODE Problems . . . . . . . . . . . 5-63 Boundary Value Problem Solver . . . . . . . . . . . . . . . . . . . . . . . . 5-64 Changing BVP Integration Properties . . . . . . . . . . . . . . . . . . . 5-67 Solving BVP Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-68 Using Continuation to Make a Good Initial Guess . . . . . . . . . 5-72 Solving Singular BVPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-80 Solving Multipoint BVPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-84 Partial Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . 5-89 PDE Function Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-89 Introduction to PDE Problems . . . . . . . . . . . . . . . . . . . . . . . . . 5-90 MATLAB Partial Differential Equation Solver . . . . . . . . . . . . 5-91 Solving PDE Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-94 Evaluating the Solution at Specific Points . . . . . . . . . . . . . . . . 5-99 Changing PDE Integration Properties . . . . . . . . . . . . . . . . . . 5-100 Example: Electrodynamics Problem . . . . . . . . . . . . . . . . . . . . 5-100 Selected Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-106 iv Contents
6 Sparse Matrices Function Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-5 Sparse Matrix Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-5 General Storage Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-6 Creating Sparse Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-7 Importing Sparse Matrices from Outside MATLAB . . . . . . . . 6-12 Viewing Sparse Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-13 Information About Nonzero Elements . . . . . . . . . . . . . . . . . . . 6-13 Viewing Sparse Matrices Graphically . . . . . . . . . . . . . . . . . . . 6-15 The find Function and Sparse Matrices . . . . . . . . . . . . . . . . . . 6-16 Adjacency Matrices and Graphs . . . . . . . . . . . . . . . . . . . . . . . 6-17 Introduction to Adjacency Matrices . . . . . . . . . . . . . . . . . . . . . 6-17 Graphing Using Adjacency Matrices . . . . . . . . . . . . . . . . . . . . 6-18 The Bucky Ball . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-18 An Airflow Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-23 Sparse Matrix Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-25 Computational Considerations . . . . . . . . . . . . . . . . . . . . . . . . . 6-25 Standard Mathematical Operations . . . . . . . . . . . . . . . . . . . . . 6-25 Permutation and Reordering . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-26 Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-30 Simultaneous Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . 6-36 Eigenvalues and Singular Values . . . . . . . . . . . . . . . . . . . . . . . 6-39 Performance Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-41 Selected Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-44 Index v
Page 1 and 2: MATLAB® The Language of Technical
Page 3: Revision History June 2004 First pr
Page 6 and 7: 2 Polynomials and Interpolation Pol
Page 10 and 11: vi Contents
Page 12 and 13: 1 Matrices and Linear Algebra Funct
Page 14 and 15: 1 Matrices and Linear Algebra Matri
Page 16 and 17: 1 Matrices and Linear Algebra Addin
Page 18 and 19: 1 Matrices and Linear Algebra If x
Page 20 and 21: 1 Matrices and Linear Algebra y = v
Page 22 and 23: 1 Matrices and Linear Algebra Vecto
Page 24 and 25: 1 Matrices and Linear Algebra backs
Page 26 and 27: 1 Matrices and Linear Algebra If A
Page 28 and 29: 1 Matrices and Linear Algebra You c
Page 30 and 31: 1 Matrices and Linear Algebra 0.9 0
Page 32 and 33: 1 Matrices and Linear Algebra Inver
Page 34 and 35: 1 Matrices and Linear Algebra X = p
Page 36 and 37: 1 Matrices and Linear Algebra There
Page 38 and 39: 1 Matrices and Linear Algebra The e
Page 40 and 41: 1 Matrices and Linear Algebra The L
Page 42 and 43: 1 Matrices and Linear Algebra In co
Page 44 and 45: 1 Matrices and Linear Algebra Matri
Page 46 and 47: 1 Matrices and Linear Algebra compu
Page 48 and 49: 1 Matrices and Linear Algebra Eigen
Page 50 and 51: 1 Matrices and Linear Algebra produ
Page 52 and 53: 1 Matrices and Linear Algebra Singu
Page 54 and 55: 1 Matrices and Linear Algebra 1-44
Page 56 and 57: 2 Polynomials and Interpolation Pol
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2 Polynomials and Interpolation pol
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2 Polynomials and Interpolation Cal
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2 Polynomials and Interpolation whe
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2 Polynomials and Interpolation Int
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2 Polynomials and Interpolation int
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2 Polynomials and Interpolation 2 G
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2 Polynomials and Interpolation for
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2 Polynomials and Interpolation Con
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2 Polynomials and Interpolation Lat
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2 Polynomials and Interpolation −
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2 Polynomials and Interpolation −
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2 Polynomials and Interpolation 7 3
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2 Polynomials and Interpolation T =
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2 Polynomials and Interpolation Bec
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2 Polynomials and Interpolation 2-3
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2 Polynomials and Interpolation 2-3
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3 Fast Fourier Transform (FFT) Intr
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3 Fast Fourier Transform (FFT) 200
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3 Fast Fourier Transform (FFT) 2 x
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3 Fast Fourier Transform (FFT) 500
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3 Fast Fourier Transform (FFT) Func
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4 Function Functions Function Summa
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4 Function Functions You can also c
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4 Function Functions 25 20 15 10 5
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4 Function Functions Minimizing Fun
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4 Function Functions To try fminsea
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4 Function Functions Plotting the R
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4 Function Functions The number of
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4 Function Functions and displays t
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4 Function Functions end function s
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4 Function Functions States of the
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4 Function Functions 100 80 60 40 2
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4 Function Functions You can verify
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4 Function Functions Troubleshootin
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4 Function Functions A three-dimens
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4 Function Functions Parameterizing
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4 Function Functions “Anonymous F
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5 Differential Equations Initial Va
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5 Differential Equations odephas3 o
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5 Differential Equations This secti
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5 Differential Equations The basic
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5 Differential Equations 2 Code the
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5 Differential Equations function.
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5 Differential Equations One way to
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5 Differential Equations y0, yp0 Ve
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5 Differential Equations For exampl
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5 Differential Equations 1 0.8 0.6
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5 Differential Equations 2.5 Soluti
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5 Differential Equations To run thi
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5 Differential Equations 2 u′ i =
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5 Differential Equations dydt(i+1,:
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5 Differential Equations refine = 4
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5 Differential Equations Example: A
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5 Differential Equations function [
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5 Differential Equations Note The R
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5 Differential Equations 1 Robertso
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5 Differential Equations The MATLAB
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5 Differential Equations Summary of
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5 Differential Equations Problem Si
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5 Differential Equations Error Tole
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5 Differential Equations Troublesho
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5 Differential Equations Function d
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5 Differential Equations dde23 prod
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5 Differential Equations The exampl
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5 Differential Equations solution y
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5 Differential Equations Example: C
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5 Differential Equations Changing D
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5 Differential Equations BVP Functi
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5 Differential Equations two-point
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5 Differential Equations The input
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5 Differential Equations 2 Pass the
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5 Differential Equations Finding Un
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5 Differential Equations vectorized
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5 Differential Equations There is a
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5 Differential Equations 3 Solve on
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5 Differential Equations hold off T
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5 Differential Equations Note The d
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5 Differential Equations legend('An
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5 Differential Equations Here, v(1-
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5 Differential Equations solution v
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5 Differential Equations Note The D
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5 Differential Equations After disc
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5 Differential Equations The output
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5 Differential Equations Note See t
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5 Differential Equations The exampl
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5 Differential Equations and the ri
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5 Differential Equations u1(x,t) 1
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5 Differential Equations Selected B
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6 Sparse Matrices Function Summary
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6 Sparse Matrices Function Summary
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6 Sparse Matrices This matrix requi
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6 Sparse Matrices S = (3,1) 1 (2,2)
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6 Sparse Matrices Now F = full(S) d
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6 Sparse Matrices Importing Sparse
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6 Sparse Matrices west0479 west0479
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6 Sparse Matrices The find Function
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6 Sparse Matrices of the rows and c
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6 Sparse Matrices The vertices of o
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6 Sparse Matrices 0 10 20 30 40 50
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6 Sparse Matrices 0 500 1000 1500 2
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6 Sparse Matrices simply sparse(m,n
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6 Sparse Matrices Similarly, S(:,p)
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6 Sparse Matrices The following MAT
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6 Sparse Matrices 0 Original 0 Reve
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6 Sparse Matrices QR Factorization
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6 Sparse Matrices shows that A has
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6 Sparse Matrices Functions for Ite
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6 Sparse Matrices set up the five-p
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6 Sparse Matrices Manipulating Spar
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6 Sparse Matrices Selected Bibliogr
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Index comparing sparse and full mat
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Index H hb1dae demo 5-35 hb1ode dem
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Index nonstiff ODE examples rigid b
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Index LU factorization 6-30 minimum
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Index twobvp demo 5-63 two-dimensio
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MATLAB Mathematics - SERC - Index of

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