Local Error-- Numerical Analysis (computer science) Just show how the local error is 28% (.. the part marked in red box). Local error I believe you would need to use local truncation error (Taylor Series) Euler's Method Solve numerically: dy/dx = -2x^3 + 12x^2 - 20x + 8.5 From x = 0 to x = 4 with step size h = 0.5 initial condition:(x = 0; y = 1) y = -0.5x^4 + 4x^3 - 10x^2 + 8.5x + 1 y_1 + 1 = y_i + f(x_i, y_i) Delta x y(0.5) = y(0) + f(0, 1) 0.5 = 1.8.5 * 0.5 = 5.25 y(1) = y(0.5) + f(0.5, 5.25) 0.5 = 5.25 + [-2(0.5)^3 + 12(0.5)^2 - 20(0.5) + 8.5]*5 0.5 = 5.25 + 0.625 = 5.875 (true solution at x=l is y(l) = 3 and epsilon_t = 96%) y(1.5) = y(l)+f(1, 5.875)0.5 = 5.125