Temperature Distribution. The temperature distribution in a thin metal plate with constant...

Temperature Distribution. The temperature distribution in a thin metal plate with constant (or isothermal) temperatures on each side can be modeled using a two-dimensional grid, as shown in Figure. Typically, the number of points in the grid are specified, as are the constant temperatures on the four sides. The temperatures of the interior points are usually initialized to zero, but they change according to the temperatures around them. Assume that the temperature of an interior point can be computed as the average of the four adjacent temperatures; the points shaded in Figure represent the adjacent temperatures for the point labeled x in the grid. Each time that the temperature of an interior point changes, the temperatures of the points adjacent to it change. These changes continue until a thermal equilibrium is achieved and all temperatures become constant.

Figure: Temperature grid in a metal plate.

Modify the program in Problem so that two arrays are used and so that the program can perform the updates as if they all happen at the same time. Thus, all temperatures are updated using one set of array values. The two arrays are needed so that all the old temperatures are available to compute each new temperature.

Problem

Temperature Distribution. The temperature distribution in a thin metal plate with constant (or isothermal) temperatures on each side can be modeled using a two-dimensional grid, as shown in Figure. Typically, the number of points in the grid are specified, as are the constant temperatures on the four sides. The temperatures of the interior points are usually initialized to zero, but they change according to the temperatures around them. Assume that the temperature of an interior point can be computed as the average of the four adjacent temperatures; the points shaded in Figure represent the adjacent temperatures for the point labeled x in the grid. Each time that the temperature of an interior point changes, the temperatures of the points adjacent to it change. These changes continue until a thermal equilibrium is achieved and all temperatures become constant.

Figure: Temperature grid in a metal plate.

Write a program to model this temperature distribution for a grid with six rows and eight columns. Allow the user to enter the temperatures for the four sides. Use one array to store the temperatures. Thus, when a point is updated, its new value is used to update the next point. Continue updating the points, moving across the rows until the temperature differences for all updates are less than a user-entered tolerance value.