Mathematics

ODE Function Summary

Initial Value ODE Problem Solvers

These are the initial value problem solvers. The table lists 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
ode23tb	Stiff differential equations	TR-BDF2

ODE Solution Evaluation

If you call an ODE solver with one output argument, it returns a structure that you can use to evaluate the solution at any point on the interval of integration.

Function	Description
deval	Evaluate the numerical solution using output of ODE solvers.

ODE Solver Properties Handling

An options structure contains named integration properties whose values are passed to the solver, and which affect problem solution. Use these functions to create, alter, or access an options structure.

Function	Description
odeset	Create or alter options structure for input to ODE solvers.
odeget	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	Description
odeplot	Time-series plot
odephas2	Two-dimensional phase plane plot
odephas3	Three-dimensional phase plane plot
odeprint	Print to command window

ODE Initial Value Problem Examples

These examples illustrate the kinds of problems you can solve in MATLAB. 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	Description
amp1dae	Stiff DAE - electrical circuit
ballode	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	Stiff problem with a time-dependent mass matrix - finite element method
fem2ode	Stiff problem with a constant mass matrix - finite element method
hb1dae	Stiff DAE from a conservation law
hb1ode	Stiff problem solved on a very long interval - Robertson chemical reaction
orbitode	Advanced event location - restricted three body problem
rigidode	Nonstiff problem - Euler equations of a rigid body without external forces
vdpode	Parameterizable van der Pol equation (stiff for large )

Initial Value Problems for ODEs and DAEs

Introduction to Initial Value ODE Problems