A square metal plate has a constant temperature on each of its four sides as shown in Figure 1. Figure 1. Figure 2. Method: We approximate the temperature distribution in the interior of the plate by calculating the temperature at a finite number of grid points. (The finer the grid, the better the approximation. ) In this project we will use a 4 times 4 grid with nine interior points as shown in Figure 2. At each of these interior points, the temperature is assumed to be the average of the temperatures at the four closest neighboring points. For example, the temperature at the point is given by T1 = 1/4 (50 + 100 + T2 + T4). Write down the system of linear equations for the temperatures at the interior points. Solve the system using the SOR method, experimenting with a range of parameters. Since the approximation is rather coarse, find the temperatures to the nearest tenth of a degree only. How do you think the SOR method on the general problem, might compare with using Gaussina elimination?
Show transcribed image textA square metal plate has a constant temperature on each of its four sides as shown in Figure 1. Figure 1. Figure 2. Method: We approximate the temperature distribution in the interior of the plate by calculating the temperature at a finite number of grid points. (The finer the grid, the better the approximation. ) In this project we will use a 4 times 4 grid with nine interior points as shown in Figure 2. At each of these interior points, the temperature is assumed to be the average of the temperatures at the four closest neighboring points. For example, the temperature at the point is given by T1 = 1/4 (50 + 100 + T2 + T4). Write down the system of linear equations for the temperatures at the interior points. Solve the system using the SOR method, experimenting with a range of parameters. Since the approximation is rather coarse, find the temperatures to the nearest tenth of a degree only. How do you think the SOR method on the general problem, might compare with using Gaussina elimination?