Solved: Use the Nonlinear Finite-Difference Algorithm with TOL = 104 to approximate the

Chapter 11, Problem 11.4.4

(choose chapter or problem)

Use the Nonlinear Finite-Difference Algorithm with TOL = 104 to approximate the solution to the following boundary-value problems. The actual solution is given for comparison to your results. a. y = y3 yy , 1 x 2, y(1) = 1 2 , y(2) = 1 3 ; use h = 0.1; actual solution y(x) = (x + 1)1. b. y = 2y3 6y 2x 3, 1 x 2, y(1) = 2, y(2) = 5 2 ; use h = 0.1; actual solution y(x) = x + x1. c. y = y + 2(y ln x)3 x1, 2 x 3, y(2) = 1 2 + ln 2, y(3) = 1 3 + ln 3; use h = 0.1; actual solution y(x) = x1 + ln x. d. y = x 2(y )2 9y2 + 4x 6 /x 5, 1 x 2, y(1) = 0, y(2) = ln 256; use h = 0.05; actual solution y(x) = x 3 ln x.