# OOF2: The Manual

## Name

2nd order Runge-Kutta (RK2) — Second order Runge-Kutta time stepping.

RK2()

## Description

RK2 is a TimeStepper that implements the second order Runge-Kutta method for solving ordinary differential equations. The error on each step is of order . RK2 is also referred to as the midpoint method.

Given a vector of unknowns (i.e. Field values in OOF2) at time , and the first order differential equation

 (6.155)

the second order Runge-Kutta estimate for is given by

 (6.156)

where .

RK2 can be applied to second order equations by using equation (6.141).

Because the method is explicit ( doesn't appear as an argument to ), equation (6.156) doesn't require a nonlinear solver even if is nonlinear.