rk.pdf

RK:

Runge-Kutta ODE Solvers

MATH1902: Numerical Solution of Differential Equations

http://people.sc.fsu.edu/∼jburkardt/classes/math1902 2020/rk/rk.pdf

A fourth order Runge Kutta step involves several initial test steps.

ODE’s by a Runge-Kutta method

If the Euler method requires too many steps, we can select a more accurate solver from the Runge-

Kutta family.

1 How accurate is the Euler method?

0

call dt or h, the method produces the approximation (t

1

, y

1

) for the next time, where

t

1

= t

0

1

= y

0

);

Now where did the Euler estimate come from? Let’s suppose the exact solution y(t) of the ODE is “reasonably

smooth” - in this case, assume it has at least two continuous derivatives over the time interval we are interested

in. Then by Taylor’s theorem we have