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The (m 1) x (m 1) tridiagonal matrix 1 +2ff A = a 0 a 1 + 2a O;; ff 0 0' 0 a a 1 + 2a is

Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden ISBN: 9781305253667 457

Solution for problem 19 Chapter 9.3

Numerical Analysis | 10th Edition

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Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden

Numerical Analysis | 10th Edition

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Problem 19

The (m 1) x (m 1) tridiagonal matrix 1 +2ff A = a 0 a 1 + 2a O;; ff 0 0' 0 a a 1 + 2a is involved in the Backward Difference method to solve the heat equation. (See Section 12.2.) For the stability ofthe method, we need p(A -1) < I. With m = 11, approximate p(A~l ) for each of the following. a. b. c. a = | When is the method stable?

Step-by-Step Solution:
Step 1 of 3

• • t \ -. LA + +- --- ------- ---~:::::::::;.;;c~=-~ ~'-:-- ------ - - • --- -1- +----------'~--,L.,J..~ ~ --------- - -- - --+-- - ----------------- - --- -+-: --- -----:--- --:--------:-- - -- • ,, . . .. ; .

Step 2 of 3

Chapter 9.3, Problem 19 is Solved
Step 3 of 3

Textbook: Numerical Analysis
Edition: 10
Author: Richard L. Burden J. Douglas Faires, Annette M. Burden
ISBN: 9781305253667

Numerical Analysis was written by and is associated to the ISBN: 9781305253667. Since the solution to 19 from 9.3 chapter was answered, more than 234 students have viewed the full step-by-step answer. The answer to “The (m 1) x (m 1) tridiagonal matrix 1 +2ff A = a 0 a 1 + 2a O;; ff 0 0' 0 a a 1 + 2a is involved in the Backward Difference method to solve the heat equation. (See Section 12.2.) For the stability ofthe method, we need p(A -1) < I. With m = 11, approximate p(A~l ) for each of the following. a. b. c. a = | When is the method stable?” is broken down into a number of easy to follow steps, and 77 words. This full solution covers the following key subjects: . This expansive textbook survival guide covers 76 chapters, and 1204 solutions. This textbook survival guide was created for the textbook: Numerical Analysis, edition: 10. The full step-by-step solution to problem: 19 from chapter: 9.3 was answered by , our top Math solution expert on 03/16/18, 03:24PM.

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The (m 1) x (m 1) tridiagonal matrix 1 +2ff A = a 0 a 1 + 2a O;; ff 0 0' 0 a a 1 + 2a is