`ode23tb`

TR-BDF2 solver for stiff differential equations at crude tolerances.

Category: Mathematics > Numerical Integration and Differential Equations

Syntax

[t, y] = ode23tb(odefun, tspan, y0)

Integrates y' = odefun(t, y).

[t, y] = ode23tb(odefun, tspan, y0, options)

Also applies options from odeset.

Description

Each step combines a trapezoidal-rule stage with a second-order backward differentiation stage, using the same iteration matrix for both. The method is implicit and L-stable, so it damps stiff components well.

Like ode23s, it can beat ode15s when the tolerances are loose.

Input arguments

odefun: Handle dydt = odefun(t, y).
tspan: [t0 tf] or a vector of output times.
y0: Vector of initial values.

Output arguments

t, y: Time points and solution, laid out as for ode45.

Example

Stiff decay

f = @(t, y) -100*(y - cos(t));
[t, y] = ode23tb(f, [0 1], 0);
fprintf('%.3f\n', y(end))

Output

0.549

ode23tb