Implicit Euler Method

Differential Equations

The Implicit Euler method is a method for solving differential equations. It uses the fundamental theorem of calculus combined with root-finding to solve differential equations.

Derivation

We start with the fundamental theorem of calculus

y (t_{n + 1}) - y (t_{n}) = \int_{t_{n}}^{t_{n + 1}} y^{'} (t) d t

While the method is written such that it is applicable to first order equations, it also can be used to solve higher order equations.