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5 Differential Equations Initial Value Problems for ODEs and DAEs This section describes how to use MATLAB to solve initial value problems (IVPs) of ordinary differential equations (ODEs) and differential-algebraic equations (DAEs). This section covers the following topics: • “ODE Function Summary” on page 5-2 • “Introduction to Initial Value ODE Problems” on page 5-4 • “Solvers for Explicit and Linearly Implicit ODEs” on page 5-5 • “Examples: Solving Explicit ODE Problems” on page 5-9 • “Solver for Fully Implicit ODEs” on page 5-15 • “Example: Solving a Fully Implicit ODE Problem” on page 5-16 • “Changing ODE Integration Properties” on page 5-17 • “Examples: Applying the ODE Initial Value Problem Solvers” on page 5-18 • “Questions and Answers, and Troubleshooting” on page 5-43 ODE Function Summary ODE Initial Value Problem Solvers The following table lists the initial value problem solvers, the kind of problem you can solve with each solver, and the method each solver uses. Solver Solves These Kinds of Problems Method ode45 Nonstiff differential equations Runge-Kutta ode23 Nonstiff differential equations Runge-Kutta ode113 Nonstiff differential equations Adams ode15s Stiff differential equations and DAEs NDFs (BDFs) ode23s Stiff differential equations Rosenbrock ode23t Moderately stiff differential equations and DAEs Trapezoidal rule 5-2
Initial Value Problems for ODEs and DAEs ode23tb Stiff differential equations TR-BDF2 ode15i Fully implicit differential equations BDFs ODE Solution Evaluation and Extension You can use the following functions to evaluate and extend solutions to ODEs. Function deval odextend Description Evaluate the numerical solution using the output of ODE solvers. Extend the solution of an initial value problem for an ODE ODE Solvers Properties Handling An options structure contains named properties whose values are passed to ODE solvers, and which affect problem solution. Use these functions to create, alter, or access an options structure. Function odeset odeget Description Create or alter options structure for input to ODE solver. Extract properties from options structure created with odeset. ODE Solver Output Functions If an output function is specified, the solver calls the specified function after every successful integration step. You can use odeset to specify one of these sample functions as the OutputFcn property, or you can modify them to create your own functions. Function odeplot odephas2 Description Time-series plot Two-dimensional phase plane plot 5-3
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1 Matrices and Linear Algebra Funct
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6 Sparse Matrices Function Summary
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Index H hb1dae demo 5-35 hb1ode dem
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Index LU factorization 6-30 minimum
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