Answer: Use the Piecewise Linear Algorithm to approximate the solutions to the following

Chapter 11, Problem 3

(choose chapter or problem)

Use the Piecewise Linear Algorithm to approximate the solutions to the following boundary-value problems, and compare the results to the actual solution: a. x2y 2xy + 2y = 4x2, 0 x 1, y(0) = y(1) = 0; use h = 0.1; actual solution y(x) = x2 x. b. d dx (ex y ) + ex y = x + (2 x)ex , 0 x 1, y(0) = y(1) = 0; use h = 0.1; actual solution y(x) = (x 1)(ex 1). c. d dx (ex y ) + ex y = (x 1) (x + 1)e(x1) , 0 x 1, y(0) = y(1) = 0; use h = 0.05; actual solution y(x) = x(ex e). d. (x + 1)y y + (x + 2)y = [2 (x + 1)2]e ln 2 2ex , 0 x 1, y(0) = y(1) = 0; use h = 0.05; actual solution y(x) = ex ln(x + 1) (e ln 2)x. 4. Use