Euler's method is a numerical approximation technique used to estimate the solution of a differential equation. It is often used when the equation cannot be solved using traditional analytical methods.
Euler's method works by breaking down a differential equation into smaller intervals and approximating the solution at each interval using the slope of the equation at that point. By repeating this process, a numerical solution can be obtained.
Euler's method is a first-order approximation, which means it may not be accurate when the interval size is too large. It also assumes a constant slope between two points, which may not always be the case.
The accuracy of Euler's method can be improved by decreasing the interval size and using a smaller time step. Other more advanced numerical methods such as Runge-Kutta methods can also be used to improve accuracy.
Euler's method is commonly used in physics, engineering, and other scientific fields where differential equations are present. It is also used in computer graphics and simulations to model continuous motion and changes.