The (m 1) x (w 1) tridiagonal matrix 1 - 2a a 0 0 2 -1 0 0 -1 2 -1 0 0 -1 2 -1 0 0 -1 2
Chapter 9, Problem 8(choose chapter or problem)
The (m 1) x (w 1) tridiagonal matrix 1 - 2a a 0 0 2 -1 0 0 -1 2 -1 0 0 -1 2 -1 0 0 -1 2 A = a 0 0' a 1 - 2a a 0 a ' 0 a I - 2a is involved in the Forward Difference method to solve the heat equation (see Section 12.2). For the stability ofthe method, we need p(A) < 1. With m = 11, approximate the eigenvalues of A for each of the following. a. 1 a - 4 b. 1 a 2 c. 3 a - 4 When is the method stable?
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