# Define the derivative, dy/dx function dydx(x, y) return -2.0 * x * y end # Euler method: compute y(x+h) function euler_method(y, x, h) return y + dydx(x, y) * h end # Solve the differential equation from x=a to x=b with n discretized points a = 0.0 b = 2.5 n = 8 h = (b - a) / n x_values = range(a, stop=b, length=n+1) y_values = zeros(n+1) y_exact = zeros(n+1) # Initial condition, y(a)=y_0 y_values[1] = 1.0 y_exact[1] = 1.0 for i in 1:n y_values[i+1] = euler_method(y_values[i], x_values[i], h) y_exact[i+1] = exp(-x_values[i]^2) end println( length(y_values))