Summary of ODE Options

Solving ODEs frequently requires fine-tuning parameters, adjusting error tolerances, or passing additional information to the solver. This topic shows how to specify options, and which differential equation solvers each option is compatible with.

Options Syntax

Use the odeset function to create an options structure that you then pass to the solver as the fourth input argument. For example, to adjust the relative and absolute error tolerances:

opts = odeset('RelTol',1e-2,'AbsTol',1e-5);
[t,y] = ode45(@odefun,tspan,y0,opts);

If you use the command odeset with no inputs, then MATLAB^® displays a list of the possible values for each option, with default values indicated by curly braces {}.

The odeget function queries the value of an option in an existing structure, which you can use to dynamically change option values based on conditions. For example, this code detects whether Stats is set to 'on', and changes the value if necessary:

if isempty(odeget(opts,'Stats'))
  odeset(opts,'Stats','on')
end

Compatibility of Options with Each Solver

Some options in odeset are generic and compatible with any solver, while others are solver-specific. This table summarizes the compatibility of each option with the different solvers.

Option	`ode45`	`ode23`	`ode113`	`ode15s`	`ode23s`	`ode23t`	`ode23tb`	`ode15i`
`RelTol AbsTol NormControl`	✓	✓	✓	✓	✓	✓	✓	✓
`OutputFcn OutputSel Refine Stats`	✓	✓	✓	✓	✓	✓	✓	✓
`NonNegative`	✓	✓	✓	✓*	—	✓*	✓*	—
`Events`	✓	✓	✓	✓	✓	✓	✓	✓**
`MaxStep InitialStep`	✓	✓	✓	✓	✓	✓	✓	✓
`Jacobian JPattern Vectorized`	—	—	—	✓	✓	✓	✓	✓
`Mass MStateDependence MvPattern MassSingular`	✓ ✓ — —	✓ ✓ — —	✓ ✓ — —	✓ ✓ ✓ ✓	✓ — — —	✓ ✓ ✓ ✓	✓ ✓ ✓ —	— — — —
`InitialSlope`	—	—	—	✓	—	✓	—	—
`MaxOrder BDF`	—	—	—	✓	—	—	—	✓ —

* Use the NonNegative parameter with ode15s, ode23t, and ode23tb only for those problems in which there is no mass matrix.

** The events function for ode15i must accept a third input argument for yp.

Usage Examples

MATLAB includes several example files that show how to use various options. For example, type edit ballode to see an example that uses 'Events' to specify an events function, or edit batonode to see an example that uses 'Mass' to specify a mass matrix. For a complete summary of example files and which options they use, see Summary of ODE Examples and Files.

Documentation