MATLAB Mathematics - SERC - Index of

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5 Differential Equations BVP Function Summary ODE Boundary Value Problem Solver Solver bvp4c Description Solve boundary value problems for ordinary differential equations. BVP Helper Functions Function bvpinit deval Description Form the initial guess for bvp4c. Evaluate the numerical solution using the output of bvp4c. BVP Solver Properties Handling An options structure contains named properties whose values are passed to bvp4c, and which affect problem solution. Use these functions to create, alter, or access an options structure. Function bvpset bvpget Description Create/alter the BVP options structure. Extract properties from options structure created with bvpset. ODE Boundary Value Problem Examples These examples illustrate the kind of problems you can solve using the BVP solver. Click the example name to see the code in an editor. Type the example name at the command line to run it. 5-62
Boundary Value Problems for ODEs Note The Differential Equations Examples browser enables you to view the code for the BVP examples, and also run them. Click on the link to invoke the browser, or type odeexamples('bvp')at the command line. Example emdenbvp fsbvp mat4bvp Description Emden's equation, a singular BVP Falkner-Skan BVP on an infinite interval Fourth eigenfunction of Mathieu’s equation shockbvp Solution with a shock layer near x = 0 twobvp threebvp BVP with exactly two solutions Three-point boundary value problem Additional examples are provided by “Tutorial on Solving BVPs with BVP4C,” available at http://www.mathworks.com/bvp_tutorial. Introduction to Boundary Value ODE Problems The BVP solver is designed to handle systems of ordinary differential equations y′ = fxy ( , ) where x is the independent variable, y is the dependent variable, and y′ represents dy ⁄ dx . See “What Is an Ordinary Differential Equation?” on page 5-4 for general information about ODEs. Using Boundary Conditions to Specify the Solution of Interest In a boundary value problem, the solution of interest satisfies certain boundary conditions. These conditions specify a relationship between the values of the solution at more than one x . In its basic syntax, bvp4c is designed to solve 5-63
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MATLAB® The Language of Technical
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Revision History June 2004 First pr
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2 Polynomials and Interpolation Pol
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Introduction to Initial Value ODE P
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vi Contents
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1 Matrices and Linear Algebra Funct
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1 Matrices and Linear Algebra Matri
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1 Matrices and Linear Algebra Addin
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1 Matrices and Linear Algebra If x
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1 Matrices and Linear Algebra y = v
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1 Matrices and Linear Algebra Singu
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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 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 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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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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