Euler's Method is a numerical approach for approximating the solution to a first-order differential equation. It involves breaking down the continuous function into smaller intervals and using linear approximations to estimate the solution at each interval.
The equation used in Euler's Method is dy/dt = f(t,y), where t represents the independent variable, y represents the dependent variable, and f(t,y) is the differential equation to be solved.
To use Euler's Method, you first need to determine the initial condition for the differential equation, which is the value of y at t=0. Then, you divide the interval of t into smaller intervals, and use the following formula to approximate the solution at each interval: yn+1 = yn + f(tn, yn) * Δt. Repeat this process until you reach the desired value of t.
Euler's Method is used when it is not possible to find the exact solution to a differential equation. It provides a close approximation to the solution and can be used to solve a wide range of differential equations.
Euler's Method is a first-order approximation and can introduce errors in the solution, especially for large intervals or when the function has large changes. It also does not guarantee the convergence of the solution and can give inaccurate results for certain types of differential equations.