`ode23`

Low-order Runge-Kutta solver for nonstiff differential equations.

Category: Mathematics > Numerical Integration and Differential Equations

Syntax

[t, y] = ode23(odefun, tspan, y0)

Integrates y' = odefun(t, y) over tspan from y0.

[t, y] = ode23(odefun, tspan, y0, options)

Also applies options from odeset.

sol = ode23(___)

Returns a structure for use with deval.

Description

ode23 pairs a second-order and a third-order Runge-Kutta formula to estimate the error and adapt the step. It is cheaper per step than ode45 but needs more steps for a given accuracy, so it is the better choice for crude tolerances or for mildly stiff problems.

When tspan has only two entries, the solver returns the points it chose; with more entries, it returns the solution at exactly those times.

Input arguments

odefun: Handle dydt = odefun(t, y) returning a column vector.
tspan: [t0 tf], or a longer vector of times at which to report the solution.
y0: Vector of initial values.
options: Structure from odeset.

Output arguments

t: Column vector of time points.
y: Array with one row per time and one column per component.

Example

Exponential decay

[t, y] = ode23(@(t, y) -y, [0 1], 1);
fprintf('%.4f %.4f\n', y(end), exp(-1))

Output

0.3679 0.3679

ode23