When given the initial values for
Here,
The Euler’s method is explicit, meaning the solution
Generalization to Higher-order Process
While the Euler method is typically used to solve first-order ODEs, any ODE of order
Variation
In addition to the explicit Euler method, there are two other variations of Euler methods that offer different trade-offs:
- symplectic Euler’s method (also called semi-implict Euler method)
- implicit Euler’s method (also called backward Euler method)
- more stable but requires to solve an algebraic equation