odeset (MATLAB Functions)

Create or alter options structure for input to ordinary differential equation (ODE) solvers

Syntax

options = odeset('name1',value1,'name2',value2,...)
options = odeset(oldopts,'name1',value1,...)
options = odeset(oldopts,newopts)
odeset

Description

The odeset function lets you adjust the integration parameters of the ODE solvers. The ODE solvers can integrate systems of differential equations of one of these forms

See below for information about the integration parameters.

options = odeset('name1',value1,'name2',value2,...) creates an integrator options structure in which the named properties have the specified values. Any unspecified properties have default values. It is sufficient to type only the leading characters that uniquely identify a property name. Case is ignored for property names.

options = odeset(oldopts,'name1',value1,...) alters an existing options structure oldopts.

options = odeset(oldopts,newopts) alters an existing options structure oldopts by combining it with a new options structure newopts. Any new options not equal to the empty matrix overwrite corresponding options in oldopts.

odeset with no input arguments displays all property names as well as their possible and default values.

ODE Properties

The available properties depend on the ODE solver used. There are several categories of properties:

Note This reference page describes the ODE properties for MATLAB, Version 6. The Version 5 properties are supported only for backward compatibility. For information on the Version 5 properties, type at the MATLAB command line: more on, type odeset, more off.

Error Tolerance Properties
Property
Value
Description

RelTol
Positive scalar {1e-3}
A relative error tolerance that applies to all components of the solution vector. The estimated error in each integration step satisfies
|e(i)|<=max(RelTol*abs(y(i)),AbsTol(i)

AbsTol
Positive scalar or vector {1e-6}
The absolute error tolerance. If scalar, the tolerance applies to all components of the solution vector. Otherwise the tolerances apply to corresponding components.

NormControl
on | {off}
Control error relative to norm of solution. Set this property on to request that the solvers control the error in each integration step with norm(e) <= max(RelTol*norm(y),AbsTol). By default the solvers use a more stringent component-wise error control.

**Error Tolerance Properties**
Property	Value	Description
`RelTol`	Positive scalar {`1e-3`}	A relative error tolerance that applies to all components of the solution vector. The estimated error in each integration step satisfies `\|e(i)\|<=max(RelTol*abs(y(i)),AbsTol(i)`
`AbsTol`	Positive scalar or vector {`1e-6`}	The absolute error tolerance. If scalar, the tolerance applies to all components of the solution vector. Otherwise the tolerances apply to corresponding components.
`NormControl`	`on` \| {`off`}	Control error relative to norm of solution. Set this property `on` to request that the solvers control the error in each integration step with `norm(e) <= max(RelTol*norm(y),AbsTol)`. By default the solvers use a more stringent component-wise error control.

Solver Output Properties
Property
Value

Description

OutputFcn
Function
Installable output function. The ODE solvers provide sample functions that you can use or modify:

odeplot
Time series plotting (default)

odephas2
Two-dimensional phase plane plotting

odephas3
Three-dimensional phase plane plotting

odeprint
Print solution as it is computed

To create or modify an output function, see ODE Solver Output Properties in the "Differential Equations" section of the MATLAB documentation.

OutputSel
Vector of integers
Output selection indices. Specifies the components of the solution vector that the solver passes to the output function. OutputSel defaults to all components.

Refine
Positive integer
Produces smoother output, increasing the number of output points by the specified factor. The default value is 1 in all solvers except ode45, where it is 4. Refine doesn't apply if length(tspan) > 2.

Stats
on | {off}
Specifies whether the solver should display statistics about the computational cost of the integration.

**Solver Output Properties**
Property	Value		Description
`OutputFcn`	Function	Installable output function. The ODE solvers provide sample functions that you can use or modify:
		`odeplot`	Time series plotting (default)
		`odephas2`	Two-dimensional phase plane plotting
		`odephas3`	Three-dimensional phase plane plotting
		`odeprint`	Print solution as it is computed
		To create or modify an output function, see ODE Solver Output Properties in the "Differential Equations" section of the MATLAB documentation.
`OutputSel`	Vector of integers	Output selection indices. Specifies the components of the solution vector that the solver passes to the output function. `OutputSel` defaults to all components.
`Refine`	Positive integer	Produces smoother output, increasing the number of output points by the specified factor. The default value is `1` in all solvers except `ode45`, where it is `4`. `Refine` doesn't apply if `length`(`tspan`) `>` `2`.
`Stats`	`on` \| {`off`}	Specifies whether the solver should display statistics about the computational cost of the integration.

Jacobian Matrix Properties (for ode15s, ode23s, ode23t, and ode23tb)
Property
Value
Description

Jacobian
Function | constant matrix
Jacobian function. Set this property to @FJac (if a function FJac(t,y) returns ) or to the constant value of .

JPattern
Sparse matrix of {0,1}
Sparsity pattern. Set this property to a sparse matrix with if component of depends on component of , and 0 otherwise.

Vectorized
on | {off}
Vectorized ODE function. Set this property on to inform the stiff solver that the ODE function F is coded so that F(t,[y1 y2 ...]) returns the vector [F(t,y1) F(t,y2) ...]. That is, your ODE function can pass to the solver a whole array of column vectors at once. A stiff function calls your ODE function in a vectorized manner only if it is generating Jacobians numerically (the default behavior) and you have used odeset to set Vectorized to on.

**Jacobian Matrix Properties (for ode15s, ode23s, ode23t, and ode23tb)**
Property	Value	Description
`Jacobian`	Function \| constant matrix	Jacobian function. Set this property to `@FJac` (if a function `FJac(t,y)` returns ) or to the constant value of .
`JPattern`	Sparse matrix of {0,1}	Sparsity pattern. Set this property to a sparse matrix with if component of depends on component of , and 0 otherwise.
`Vectorized`	`on` \| {`off`}	Vectorized ODE function. Set this property `on` to inform the stiff solver that the ODE function `F` is coded so that `F(t,[y1 y2 ...]`) returns the vector `[F(t,y1) F(t,y2) ...]`. That is, your ODE function can pass to the solver a whole array of column vectors at once. A stiff function calls your ODE function in a vectorized manner only if it is generating Jacobians numerically (the default behavior) and you have used `odeset` to set `Vectorized` to `on`.

Event Location Property
Property
Value
Description

Events
Function
Locate events. Set this property to @Events, where Events is the name of the events function. See the ODE solvers for details.

**Event Location Property**
Property	Value	Description
`Events`	Function	Locate events. Set this property to `@Events`, where `Events` is the name of the events function. See the ODE solvers for details.

Mass Matrix and DAE-Related Properties
Property
Value
Description

Mass
Constant matrix | function
For problems set this property to the value of the constant mass matrix . For problems , set this property to @Mfun, where Mfun is a function that evaluates the mass matrix .

MStateDependence
none | {weak} | strong
Dependence of the mass matrix on . Set this property to none for problems . Both weak and strong indicate , but weak results in implicit solvers using approximations when solving algebraic equations. For use with all solvers except ode23s.

MvPattern
Sparse matrix
sparsity pattern. Set this property to a sparse matrix with if for any , the component of depends on component of , and 0 otherwise. For use with the ode15s, ode23t, and ode23tb solvers when MStateDependence is strong.

MassSingular
yes | no | {maybe}
Indicates whether the mass matrix is singular. The default value of 'maybe' causes the solver to test whether the problem is a DAE. For use with the ode15s and ode23t solvers.

InitialSlope
Vector
Consistent initial slope , where satisfies

. For use with the ode15s and ode23t solvers when solving DAEs.

**Mass Matrix and DAE-Related Properties**
Property	Value	Description
`Mass`	Constant matrix \| function	For problems set this property to the value of the constant mass matrix . For problems , set this property to `@Mfun`, where `Mfun` is a function that evaluates the mass matrix .
`MStateDependence`	`none \| {weak} \| strong`	Dependence of the mass matrix on . Set this property to `none` for problems . Both `weak` and `strong` indicate , but `weak` results in implicit solvers using approximations when solving algebraic equations. For use with all solvers except `ode23s`.
`MvPattern`	Sparse matrix	sparsity pattern. Set this property to a sparse matrix with if for any , the component of depends on component of , and 0 otherwise. For use with the `ode15s`, `ode23t`, and `ode23tb` solvers when `MStateDependence` is strong.
`MassSingular`	`yes \| no \| {maybe}`	Indicates whether the mass matrix is singular. The default value of `'maybe'` causes the solver to test whether the problem is a DAE. For use with the `ode15s` and `ode23t` solvers.
`InitialSlope`	Vector	Consistent initial slope , where satisfies . For use with the `ode15s` and `ode23t` solvers when solving DAEs.

Step Size Properties
Property
Value
Description

MaxStep
Positive scalar
An upper bound on the magnitude of the step size that the solver uses. The default is one-tenth of the tspan interval.

InitialStep
Positive scalar
Suggested initial step size. The solver tries this first, but if too large an error results, the solver uses a smaller step size. By default the solver determines an initial step size automatically.

**Step Size Properties**
Property	Value	Description
`MaxStep`	Positive scalar	An upper bound on the magnitude of the step size that the solver uses. The default is one-tenth of the `tspan` interval.
`InitialStep`	Positive scalar	Suggested initial step size. The solver tries this first, but if too large an error results, the solver uses a smaller step size. By default the solver determines an initial step size automatically.

In addition there are two options that apply only to the ode15s solver.

ode15s Properties
Property
Value
Description

MaxOrder
1 | 2 | 3 | 4 | {5}
The maximum order formula used.

BDF
on | {off}
Set on to specify that ode15s should use the backward differentiation formulas (BDFs) instead of the default numerical differentiation formulas (NDFs).

**ode15s Properties**
Property	Value	Description
`MaxOrder`	1 \| 2 \| 3 \| 4 \| {5}	The maximum order formula used.
`BDF`	`on \| {off}`	Set `on` to specify that `ode15s` should use the backward differentiation formulas (BDFs) instead of the default numerical differentiation formulas (NDFs).

See Also

deval, odeget, ode45, ode23, ode23t, ode23tb, ode113, ode15s, ode23s, @ (function handle)

odeget ones