Mathematics 
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 

Nonstiff differential equations 
RungeKutta 

Nonstiff differential equations 
RungeKutta 

Nonstiff differential equations 
Adams 

Stiff differential equations and DAEs 
NDFs (BDFs) 

Stiff differential equations 
Rosenbrock 

Moderately stiff differential equations and DAEs 
Trapezoidal rule 

Stiff differential equations 
TRBDF2 
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 

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 

Create or alter options structure for input to ODE solvers. 

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 

Timeseries plot 

Twodimensional phase plane plot 

Threedimensional phase plane plot 

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 statedependent mass matrix  motion of a baton 
brussode 
Stiff large problem  diffusion in a chemical reaction (the Brusselator) 
burgersode 
ODE with strongly statedependent mass matrix  Burger's equation solved using a moving mesh technique 
fem1ode 
Stiff problem with a timedependent 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 