15. Given y' = 1 + $, y(1) = 2, and true solution is: y(t) = tln(t) + 2t. Determine the relative error in each case. a.

[answerhappygod]

15 Given Y 1 Y 1 2 And True Solution Is Y T Tln T 2t Determine The Relative Error In Each Case A 1 (74.46 KiB) Viewed 24 times

15. Given y' = 1 + $, y(1) = 2, and true solution is: y(t) = tln(t) + 2t. Determine the relative error in each case. a. Complete four steps of Eulers method by hand with h = 1 to estimate y(1.4) b. Complete two steps of the Runge-Kutta method by hand with h = 2 to estimate y(1.4). . c. Compare the results of the Euler and Runge-Kutta approximations. Are the errors what you should have expected the error for each method to be? Explain. 16. Explicitly write down the quadratic Lagrange interpolating polynomial to approximate f(x) = x + 2/x with xo = 1, x1 = 2, x2 = 2.5. Evaluate the polynomial at x = 1.5 to approximate f(1.5). 17. Given f(x) = x3 – 5x+, explicitly write down the error term, E3(x), for the cubic Lagrange interpolating polynomial of f(x) with Xo = -1, xı = 0, X2 = 3, x3 = 4. E3(x) =