matlab4 - ( b-AT ) The value of as Ive written it depends...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 3353 Matlab Assignment 4 - Due 11/18/09 T. Hagstrom 1. Using random similarity transforms build 3 × 3 matrices, A , with the indicated eigenvalues. Then, starting with a random 3-vector, x (0) , compute x ( k ) = Ax ( k - 1) , k = 1 , . . . 25 . Plot the iterates (use plot3 ) and explain the relationship between the eigenvalues and the observed results. i. { 1 . 02 , - . 8 , . 2 } ii. n 1+ i 2 , 1 - i 2 , 1 3 o iii. ± 2+ i 3 , 2 - i 3 , - 1 2 ² 2. Consider the dynamic heat transfer problem associated with Problem 2 in Homework 2. In that problem, given a p × p lattice of temperature values, you set up and solved a system of p 2 equations AT = b where the vector b was determined by the boundary temperatures. Now suppose the temperatures evolve by the differential equation: dT j dt = - κ ³ T j - 1 4 ( T left + T right + T up + T down ) ´ where κ measures the heat conduction. In matrix form dT dt = κ
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ( b-AT ) The value of as Ive written it depends on the lattice spacing. You can take it to be = p 2 10 . 1 a. Let T s be the steady state solution as computed in Homework 2. That is AT s = b verify that if we write T ( t ) = T s + W ( t ) then dW dt =-AW, W (0) = T (0)-T s b. Use eig to compute the eigenvalues of A for p = 10. What do you conclude about the convergence of the temperature to the steady state value? c. Suppose the sample is intially heated to a temperature of 80. Use expm to compute the temper-ature at times t = . 5 : . 5 : 5 and use surf to plot it. (Note you are solving for W so you need to add in T s to get the total temperature eld. Use p = 10.) 2...
View Full Document

Page1 / 2

matlab4 - ( b-AT ) The value of as Ive written it depends...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online