`ode`

Object that describes an initial value problem and holds its solver settings.

Category: Other public functions: funfun

Syntax

f = ode

Creates an empty problem to be filled in through its properties.

f = ode(Name=Value)

Creates the problem with properties given as name-value pairs, such as ODEFcn and InitialValue.

sol = solve(f, t0, tf)

Integrates from t0 to tf and returns an ODEResults object.

Description

The ode object is the newer interface to the ODE solvers: instead of one long call to ode45 with a pile of options, the problem and its settings are stored in one object that can be inspected, changed and solved again. solve(f, t0, tf) returns an object whose Time and Solution properties hold the time points and the states, with one column per time point.

The features that older code passed through odeset are now objects of their own: odeEvent for events, odeJacobian for the Jacobian and odeMassMatrix for a mass matrix.

Input arguments

ODEFcn: Function handle @(t, y) giving the derivative of the state.
InitialValue: State at the initial time.
InitialTime: Initial time, 0 by default.
Solver: A specific solver such as 'ode15s', or 'auto' (default) to let the object choose.
RelativeTolerance, AbsoluteTolerance: Error tolerances, 1e-3 and 1e-6 by default.
Jacobian, MassMatrix, EventDefinition: Optional odeJacobian, odeMassMatrix and odeEvent objects.

Output arguments

f: An ode object. Its SelectedSolver property tells which solver 'auto' picked.

Example

Solve y' = -y

f = ode(ODEFcn=@(t, y) -y, InitialValue=1);
sol = solve(f, 0, 2);
fprintf('y(2) = %.3f\n', sol.Solution(end))
fprintf('exact  %.3f\n', exp(-2))

Output

y(2) = 0.135
exact  0.135

ode