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5 Differential Equations Summary of Code Examples The following table lists the M-files for all the ODE initial value problem examples. Click the example name to see the code in an editor. Type the example name at the command line to run it. Note The Differential Equations Examples browser enables you to view the code for the ODE examples and DAE examples. You can also run the examples from the browser. Click on these links to invoke the browser, or type odeexamples('ode')or odeexamples('dae')at the command line. Example amp1dae ballode Description Stiff DAE — electrical circuit Simple event location — bouncing ball batonode ODE with time- and state-dependent mass matrix — motion of a baton brussode Stiff large problem — diffusion in a chemical reaction (the Brusselator) burgersode ODE with strongly state-dependent mass matrix — Burger’s equation solved using a moving mesh technique fem1ode fem2ode Stiff problem with a time-dependent mass matrix — finite element method Stiff problem with a constant mass matrix — finite element method hb1ode Stiff ODE problem solved on a very long interval — Robertson chemical reaction hb1dae ihb1dae Robertson problem — stiff, linearly implicit DAE from a conservation law Robertson problem — stiff, fully implicit DAE 5-42
Initial Value Problems for ODEs and DAEs Example iburgersode kneeode orbitode rigidode Description Burgers' equation solved as implicit ODE system The “knee problem” with nonnegativity constraints Advanced event location — restricted three body problem Nonstiff problem — Euler equations of a rigid body without external forces vdpode Parameterizable van der Pol equation (stiff for large µ ) Questions and Answers, and Troubleshooting This section contains a number of tables that answer questions about the use and operation of the ODE solvers: • General ODE solver questions • Problem size, memory use, and computation speed • Time steps for integration • Error tolerance and other options • Solving different kinds of problems • Troubleshooting General ODE Solver Questions Question How do the ODE solvers differ from quad or quadl? Can I solve ODE systems in which there are more equations than unknowns, or vice versa? Answer quad and quadl solve problems of the form y′ = ft (). The ODE solvers handle more general problems y′ = fty ( , ), linearly implicit problems that involve a mass matrix Mt ( , y) y′ = ft ( , y) , and fully implicit problems ft ( , y, y′ ) = 0 . No. 5-43
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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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1 Matrices and Linear Algebra Funct
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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 100 80 60 40 2
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5 Differential Equations u1(x,t) 1
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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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