Repeat Example 31.1, but for

To calculate: The solution to the Poisson’s equation
Answer to Problem 1P
Solution: Solution to the Poisson’s equation for provided boundary equation is
Explanation of Solution
Given Information:
Poisson’s equation:
Here, function
Boundary conditions are as
The value of the uniform heat source is
Formula used:
If a differential is in the form
Calculation:
Consider the problem statement, the expression for the boundary condition is:
The Boundary condition is provided as follows:
The general solution to the differential equation is:
Differentiate it with respect to
Compares the equations with each other.
Apply the boundary condition
Apply the boundary condition
Substitute
Use the following MATLAB command to execute the code and plot the temperature as a function of position along the rod.
Now, execute the program by pressing run button. Following plot is obtained that shows the plot of temperature verses distance.
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Chapter 31 Solutions
Numerical Methods For Engineers, 7 Ed
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