A simple numerical method for solving differential equations. If $\frac{\text{d}y}{\text{d}x}=f\left(x,y\right)$ and an initial condition is known, y = y₀ when x = x₀, then Euler’s method generates a succession of approximations y_n + 1 = y_n + hf(x_n,y_n) where x_n = x₀ + nh, n ≥ 1. This takes the known starting point and moves along a straight line segment with horizontal distance h in the direction of the tangent at (x₀,y₀). The process is repeated from the new point (x₁,y₁) etc. If the step length h is small enough, the tangents are good approximations to the curve and the method will provide a reasonable accurate estimate. Compare Runge-Kutta methods.