Solved: 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. 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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