Advanced Engineering MathematicsHW # 2: Numerical and A

Advanced Engineering MathematicsHW # 2: Numerical and Analytical Solution of 1-D Heat EquationUsing the Crank-Nicolson scheme solve the heat equation in a medium confined between two insulating walls separated by a distance L and exposed to an initial temperature profile shown below. Plot the temperature profile as a function of time and space. Use Mathematica for your programming and take advantage of its capabilities for the calculations involving matrices. You can learn about the Crank-Nicolson scheme in your undergraduate Heat Transfer book among others or online at http://en.wikipedia.org/wiki/Crank%E2%80%93Nicolson_method. You also need to solve the energy equation analytically with the techniques discussed in the class and plot your numerical and analytical results in one single plot. An example of the expected output is shown below. Advanced Engineering MathematicsHW # 2: Numerical and Analytical Solution of 1-D Heat EquationUsing the Crank-Nicolson scheme solve the heat equation in a medium confined between two insulating walls separated by a distance L and exposed to an initial temperature profile shown below. Plot the temperature profile as a function of time and space. Use Mathematica for your programming and take advantage of its capabilities for the calculations involving matrices. You can learn about the Crank-Nicolson scheme in your undergraduate Heat Transfer book among others or online at http://en.wikipedia.org/wiki/Crank%E2%80%93Nicolson_method. You also need to solve the energy equation analytically with the techniques discussed in the class and plot your numerical and analytical results in one single plot. An example of the expected output is shown below.
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