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

Chapter 11, Problem 3

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Use the Piecewise Linear Algorithm to approximate the solutions to the following boundary-value problems and compare the results to the actual solution: a. x 2 y" - 2xy' + 2y = -4x2 , 0 < x < I, y(0) - y(l) = 0; use h = 0.1; actual solution y(x) x 2 x. b. -(ex y') + e x y = x + (2 - x)ex , 0 < x < I, y(0) = y(l) = 0; use /? = 0.1; actual solution y(x) = (x l)(e~x 1). c. -(e-x y')+e-x y = (x-l)-(x+l)^"1 ', 0 < x < I, y(0) = y(l) = 0; use/? = 0.05; actual solution y(x) = x(ex e). d. -(x + l)y" - y' + (x + 2)y = [2 - (x + l)2 ]f In2 - 2ex , 0 < x < 1, y(0) = y(l) = 0; use h = 0.05; actual solution y(x) = e x ln(x + I) (

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