Verification regarding Neumann conditions at time derivative

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Thread starter maistral
Start date May 12, 2019
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Conditions Derivative Neumann Time Time derivative

In summary, Neumann conditions at time derivative refer to the boundary conditions that must be satisfied when solving a partial differential equation with respect to time. Verification of these conditions is important to ensure the accuracy and reliability of the solution, which can be done by carefully checking the specified boundary conditions and comparing the numerical solution with an analytical solution. If Neumann conditions at time derivative are not satisfied, the solution may be incorrect or unstable. However, these conditions are not always necessary, as there may be cases where the solution only depends on initial conditions.

May 12, 2019

maistral

Hi, just a question regarding neumann conditions, I seem to have forgotten these things already. I think this question is answerable by a yes or a no.

So given the 2D heat equation,

If I assign a neumann condition at say, x = 0;

Does it still follow that at the derivative of t, the condition still holds? I mean:

Thank you!

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May 13, 2019

maistral

Bump :(

1. What are Neumann conditions at time derivative?

Neumann conditions at time derivative refer to the boundary conditions that must be satisfied for a partial differential equation with a time derivative term. These conditions specify how the derivative of the dependent variable with respect to time behaves at the boundaries of the domain.

2. Why is verification necessary for Neumann conditions at time derivative?

Verification is necessary to ensure that the numerical solution of a partial differential equation with Neumann conditions at time derivative is accurate and reliable. It helps to validate the mathematical model and confirm that the numerical methods used to solve the problem are appropriate.

3. How is verification performed for Neumann conditions at time derivative?

Verification is typically done by comparing the numerical solution with an analytical solution or a known exact solution, if available. The error between the two solutions is then calculated and compared to a predefined tolerance to determine the accuracy of the numerical solution.

4. What are the consequences of not satisfying Neumann conditions at time derivative?

If Neumann conditions at time derivative are not satisfied, the numerical solution of the partial differential equation may not be accurate and can lead to incorrect results. This can also affect the stability and convergence of the numerical solution, making it unreliable.

5. Are there any limitations to verifying Neumann conditions at time derivative?

Yes, there can be limitations to verifying Neumann conditions at time derivative. For example, if an analytical solution is not available, it may be difficult to determine the accuracy of the numerical solution. Additionally, the complexity of the problem and the numerical methods used can also affect the accuracy of the verification process.