What is the relation between stability criterion and time step?

In summary, the conversation discusses the relationship between the time step and the stability criterion in creating MATLAB codes for the 2D Heat diffusion equation using the Explicit Finite Method. The time step must be greater or equal to the stability criterion, which is calculated using the formula h^2/4 x alpha. The stability criterion is an important tool in analyzing numerical methods and links are provided for further understanding.
  • #1
t0mm02
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Homework Statement:: time step must be greater than stability criterion
Relevant Equations:: stability criterion= h^2/4 x alpha

Hello. I have had to do 2 MATLAB codes based on the 2D Heat diffusion equation using the Explicit Finite Method. In those codes, the time step must be greater or equal to the stability criterion. I do not understand the relationship between the time step and the stability criterion or why the time step must be equal to the stability criterion.
 
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  • #2
If this is homework perhaps you will get more feedback here if you provide a specific question with clear reference to what part of your textbook or notes you are stuck on.

If its not homework and you seek general understanding you should probably prepare to invest some time studying regions of stability as it is used as a general tool in analysis of numerical methods, and then return here with specific questions if needed.

A few links that may be relevant for stability of ODE solvers (mayby others here can provide better links for PDE's):
https://en.wikipedia.org/wiki/Euler_method#Numerical_stability
https://en.wikipedia.org/wiki/Stiff_equation
http://folk.ntnu.no/leifh/teaching/tkt4140/._main025.html
 
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Likes jim mcnamara and BvU

1. What is the stability criterion for numerical methods?

The stability criterion for numerical methods is a condition that must be met in order for the solution to remain bounded and accurate over time. It ensures that the errors introduced by the numerical method do not grow exponentially and cause the solution to become unstable.

2. How is stability related to the time step in numerical methods?

The stability of a numerical method is directly related to the size of the time step used in the calculations. A smaller time step will generally result in a more stable solution, while a larger time step may lead to instability and inaccurate results.

3. Why is it important to consider the stability criterion when choosing a time step?

If the stability criterion is not met, the solution will become unstable and the results will be unreliable. Therefore, it is crucial to consider the stability criterion when choosing a time step in order to ensure the accuracy and reliability of the numerical method.

4. How does the stability criterion vary for different numerical methods?

The stability criterion may vary for different numerical methods depending on their algorithm and the type of problem being solved. For example, implicit methods tend to have a more relaxed stability criterion compared to explicit methods.

5. Can the stability criterion be violated in certain situations?

Yes, the stability criterion can be violated in certain situations, such as when the time step is too large or when the problem being solved is highly nonlinear. In these cases, the solution may become unstable and the numerical method may fail to produce accurate results.

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