What is eulers method?

Answer 1

Euler's method is a numerical technique used to approximate solutions to ordinary differential equations (ODEs). It works by taking small steps along the curve defined by the ODE, using the slope given by the differential equation to estimate the next value. Starting from an initial condition, the method iteratively calculates subsequent points by applying the formula: ( y_{n+1} = y_n + h f(t_n, y_n) ), where ( h ) is the step size and ( f(t_n, y_n) ) represents the derivative at the current point. While simple and easy to implement, Euler's method can be inaccurate for large step sizes or highly nonlinear functions.