Euler’s Method

Explicit fixed-step solver of first order. The Euler method named after Leonard Euler is the most basic kind of explicit method for the numerical integration of ordinary differential equatioDELETEMEns.

If the initial value problem we want to approximate is defined by

 y’(t) = f(t,y(t)),    y(t_0) = y_0,

we use the first two terms of the Taylor expansion of y, which represents the linear approximation around the point (t_0, y(t_0)). One step of the Euler method from t_n to t_n+1 = t_n+h is

 y_n+1 = y_n + hf(t_n,y_n).

The Euler method can be numerically unstable, especially for stiff equations. This limitation—along with its slow convergence of error with h-means that the Euler method is not often used, except as a simple example of numerical integration.

The Butcher tableau of the Euler forward method is:

Applicable solver settings:

• Fixed-step size
• Limit data points to last

• http://en.wikipedia.org/wiki/Euler_method