Backward Euler

Topics: Numerical Methods

The Backward Euler method is a numerical technique for approximating solutions of ordinary differential equations.

For the ODE problem $\frac{dy}{dt}=f(t,y)$ with initial condition $y(t_0) = y_0$, Backward Euler advances the numerical simulation from $t_n$ to $t_{n+1}=t_n+h$ as
$y_{n+1}=y_n + h \cdot f(t_{n+1}, y_{n+1})$
The above formula can be used to compute a running integral from data.

Backward Euler is an implicit method. This is because the derivative is evaluated at a new unknown point $(t_{n+1}, y_{n+1})$. Therefore, every step usually requires solving an algebraic equation.

References

1. https://web.mit.edu/10.001/Web/Course_Notes/Differential_Equations_Notes/node3.html