Question

80° C x1 x2 x3 50° C x4 x5 x6 30° C x7 x8 x9 100° C Figure 1: Temperature distribution application A square metal plate has a constant temperature on each of its four boundaries as depicted in Figure 1. Use a grid to approximate the temperature distribution in the interior of the plate. Assume that the temperature at each interior point, xi, for i = 1,2,...,9 is the average of the temperature at the four closet of the temperatures at the four closet neighboring points. a) Setup a system of linear equations to represent the interior temperature, xi. b) By using Gauss elimination as LU factorization, determine the temperature distribution of xi, for i = 1,2,...,9 at interior points inside the plate.

          80° C
x1 x2 x3
50° C x4 x5 x6 30° C
x7 x8 x9
100° C
Figure 1: Temperature distribution application
A square metal plate has a constant temperature on each of its four boundaries as depicted in Figure 1. Use a grid to approximate the temperature distribution in the interior of the plate. Assume that the temperature at each interior point, xi, for i = 1,2,...,9 is the average of the temperature at the four closet of the temperatures at the four closet neighboring points.
a) Setup a system of linear equations to represent the interior temperature, xi.
b) By using Gauss elimination as LU factorization, determine the temperature distribution of xi, for i = 1,2,...,9 at interior points inside the plate.

80° C
x1 x2 x3
50° C x4 x5 x6 30° C
x7 x8 x9
100° C
Figure 1: Temperature distribution application
A square metal plate has a constant temperature on each of its four boundaries as depicted in Figure 1. Use a grid to approximate the temperature distribution in the interior of the plate. Assume that the temperature at each interior point, xi, for i = 1,2,...,9 is the average of the temperature at the four closet of the temperatures at the four closet neighboring points.
a) Setup a system of linear equations to represent the interior temperature, xi.
b) By using Gauss elimination as LU factorization, determine the temperature distribution of xi, for i = 1,2,...,9 at interior points inside the plate.

Added by Ernest P.

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