Given the initial-value problem 2 y' = -y + t 2 e', 1 < / < 2, y(l) = 0, with exact
Chapter 5, Problem 9(choose chapter or problem)
Given the initial-value problem 2 y' = -y + t 2 e', 1 < / < 2, y(l) = 0, with exact solution y{t) = t 2 (e' e): a. Use Taylor's method oforder two with /? = 0.1 to approximate the solution and compare it with the actual values of y. b. Use the answers generated in part (a) and linear interpolation to approximate y at the following values and compare them to the actual values of y. i. y(1.04) ii. y(1.55) Hi. yd.97) c. Use Taylor's method oforder four with h = 0.1 to approximate the solution and compare it with the actual values of y. d. Use the answers generated in part (c) and piecewise cubic Hermite interpolation to approximate y at the following values and compare them to the actual values of y. i. y(1.04) ii. yd.55) Hi. yd-97)
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