Euler discretization

1. How does Euler's method work?
2. What is the Euler's method formula?
3. Why is Euler's method inaccurate?
4. What is Euler Maruyama?

How does Euler's method work?

Methodology. In Euler's method, you can approximate the curve of the solution by the tangent in each interval (that is, by a sequence of short line segments), at steps of h . In general, if you use small step size, the accuracy of approximation increases.

What is the Euler's method formula?

dy/dx = 1.5 means that an increment of 1 in x would carry an increment of 1.5 in y, but since we are only incrementing x by 0.5, we only increment y by 0.75.

Why is Euler's method inaccurate?

Euler's Method will only be accurate over small increments and as long as our function does not change too rapidly. Consequently, we need to ensure that our step-size isn't too large or our numerical solution will be inaccurate.

What is Euler Maruyama?

In Itô calculus, the Euler–Maruyama method (also called the Euler method) is a method for the approximate numerical solution of a stochastic differential equation (SDE). It is an extension of the Euler method for ordinary differential equations to stochastic differential equations.