Local Error-- Numerical Analysis (computer science)

Just show how the local error is 28% (show all work... the part marked in red box).

Local error I believe you would need to use local truncation error (Taylor Series)

Example 1: Euler's Method Solve numerically -2x3 +12x -20x 8.5 total error local error dx euler true From x 0 to x 4 with step size h 0.5 NA NA initial condition (x 0 y 1) 0.5 5.25 3.218 63.1 63.1 95.8 1 5.875 3 28 Exact Solution: y 0.5x4 4x3 10x2 8.5x 1 1.5 5.125 2.218 131 1.41 4.5 125 20.5 Numerical Solution: i+1 yi f (x, y )Ax y(0.5)E y (0 +f(0, 1)0.5 1+8.5*0.5 5.25 h 0.5 (true solution at x 0.5 is y(0.5) 3.22 and & E63% yax- y 0.5) +f(0.5, 5.25)0.5 5.25+D-2(0.5) 3-12 (0.5)2-20 (0.5) +8.5]*0.5 5.25+0.625 5.875 (true solution at x 1 is y(1) 3 and at 96%) True solution y(1.5)- y l tf(1, 5.875 0.5 5.125 Example 1: Euler's Method Solve numerically -2x3 +12x -20x 8.5 total error local error dx euler true From x 0 to x 4 with step size h 0.5 NA NA initial condition (x 0 y 1) 0.5 5.25 3.218 63.1 63.1 95.8 1 5.875 3 28 Exact Solution: y 0.5x4 4x3 10x2 8.5x 1 1.5 5.125 2.218 131 1.41 4.5 125 20.5 Numerical Solution: i+1 yi f (x, y )Ax y(0.5)E y (0 +f(0, 1)0.5 1+8.5*0.5 5.25 h 0.5 (true solution at x 0.5 is y(0.5) 3.22 and & E63% yax- y 0.5) +f(0.5, 5.25)0.5 5.25+D-2(0.5) 3-12 (0.5)2-20 (0.5) +8.5]*0.5 5.25+0.625 5.875 (true solution at x 1 is y(1) 3 and at 96%) True solution y(1.5)- y l tf(1, 5.875 0.5 5.125