Matlab program using implicit Finite Difference

In summary, the conversation is about a person needing help writing a MATLAB program to solve a heat transfer problem implicitly. They explain that the program will involve solving for a temperature using the temperature at 3 nodes ahead and will utilize a tridiagonal matrix and the Thomas Algorithm. The person also mentions that the variables are dimensionless and provides some additional information about the problem.
  • #1
tactical
6
0
Hello,

I need help writing a MATLAB program to solve a heat transfer problem implicitly. For some reason this is very confusing to me. The problem is stated below. Any help is greatly appriciated. Let me know if you need a little more info.

I need to write a program to solve this problem. I want to solve for a temperature T(i,n) using the temperature at the 3 nodes ahead of it. Essentially it's going to be a tridiagonal matrix in which you can solve using Thomas Algorithm. I just need help writing a program to get this tridiagonal matrix.
2h2leud.jpg


Edit: Also, all variable are dimensionless, therefore time goes from 0 to 1 and x also goes from 0 to 1. time is broken up into Δn parts and x is broken up into Δi parts. λ = Δt/Δx2
 
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  • #2
I guess this might help some:

This what the PDE that was discretized

xdv71l.png
 

1. What is Matlab program using implicit Finite Difference?

Matlab program using implicit Finite Difference is a numerical method used to solve differential equations by discretizing them into a system of algebraic equations. It is considered an efficient and accurate method for solving complex differential equations that cannot be solved analytically.

2. How does implicit Finite Difference differ from explicit Finite Difference?

The main difference between implicit and explicit Finite Difference methods is the way they handle the time derivative term in the differential equation. In explicit Finite Difference, the time derivative is calculated using the values at the current time step, while in implicit Finite Difference, it is calculated using a combination of current and future time steps, making it more stable and accurate.

3. What are the advantages of using Matlab for implicit Finite Difference?

Matlab offers a user-friendly and efficient environment for implementing implicit Finite Difference methods. With its built-in functions and tools, it allows for easy manipulation and visualization of data, making it easier to analyze and debug the code. Additionally, it has a vast library of functions and toolboxes specifically designed for solving differential equations.

4. Can implicit Finite Difference be used for all types of differential equations?

Implicit Finite Difference can be used for a wide range of differential equations, including parabolic, elliptic, and hyperbolic equations. However, it may not be the most suitable method for certain types of equations, such as stiff equations, where other methods like implicit Runge-Kutta may be more efficient.

5. How can I improve the accuracy of my Matlab program using implicit Finite Difference?

To improve the accuracy of your Matlab program, you can use a smaller time step, increase the number of grid points, or use higher-order difference schemes. It is also essential to check for stability conditions and make sure the boundary conditions are accurately implemented. Additionally, using adaptive time stepping or implementing parallel computing can also improve the accuracy and efficiency of the program.

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