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Exercise 1.4.26 The steady state temperature, u, of a plate solves Laplace's equation, Au= 0. One way to approximate the solution is to divide the plate into a square mesh and require the temperature at each node to equal the average of the temperature at the four adjacent nodes. In the following picture, the numbers represent the observed temperature at the indicated nodes. Find the temperature at the interior nodes, indicated by x, y, z, and w. One of the equations is z = = (10+0+w+x). 10. 10. 20 20 ● X y Z W 0 0 .30 .30

Exercise 1.4.26 The steady state temperature, u, of a plate solves Laplace's equation, Au= 0. One way to approximate the solution is to divide the plate into a square mesh and require the temperature at each node to equal the average of the temperature at the four adjacent nodes. In the following picture, the numbers represent the observed temperature at the indicated nodes. Find the temperature at the interior nodes, indicated by x, y, z, and w. One of the equations is z = = (10+0+w+x). 10. 10. 20 20 ● X y Z W 0 0 .30 .30

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Exercise 1.4.26 The steady state temperature, u, of a plate solves Laplace's equation, Au= 0. One way to approximate the solution is to divide the plate into a square mesh and require the temperature at each node to equal the average of the temperature at the four adjacent nodes. In the following picture, the numbers represent the observed temperature at the indicated nodes. Find the temperature at the interior nodes, indicated by x, y, z, and w. One of the equations is z = (10+0+w+x). 10. 10. 20 20 X y N 0 0 W 30 30
Transcribed Image Text:Exercise 1.4.26 The steady state temperature, u, of a plate solves Laplace's equation, Au= 0. One way to approximate the solution is to divide the plate into a square mesh and require the temperature at each node to equal the average of the temperature at the four adjacent nodes. In the following picture, the numbers represent the observed temperature at the indicated nodes. Find the temperature at the interior nodes, indicated by x, y, z, and w. One of the equations is z = (10+0+w+x). 10. 10. 20 20 X y N 0 0 W 30 30
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