MATLAB, NASAs thermal protection system

[mattyboson12]

Hi, I am writing program to model the heat flow through different space shuttle tiles. I have got it working using four different methods: Forward differencing, Backward differencing, Crank-Nicolson, DuFort-Frankel and all four methods give me similar results. What are the advantages and disadvantages of each method?

 

[gtoguy97]

Forward Differencing:Advantages: Simplicity - forward differencing is the simplest method as it only requires two values from the previous time step to calculate the new value, and it is easy to implement.Disadvantages: Accuracy – forward differencing can be numerically unstable, and is not as accurate as other methods such as DuFort-Frankel or Crank-Nicolson.Backward Differencing: Advantages: Accuracy – backward differencing is more accurate than forward differencing as it takes into account data from two time steps.Disadvantages: Complexity – backward differencing is more complex, as it requires four values from the previous time step to calculate the new value.Crank-Nicolson:Advantages: Accuracy – Crank-Nicolson is highly accurate and is considered the most reliable method for solving heat transfer problems.Disadvantages: Complexity – Crank-Nicolson is complex and difficult to implement.DuFort-Frankel: Advantages: Accuracy – DuFort-Frankel is very accurate and can handle non-linear problems.Disadvantages: Complexity – DuFort-Frankel is complex and requires a lot of computing power to solve.