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Order of boundary conditions in a Partial Differential Equation

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Old   August 2, 2010, 15:28
Default Order of boundary conditions in a Partial Differential Equation
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Gaurav
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Is it mathematically incorrect to have a 3rd order boundary condition for a 2nd order Partial Differential Equation?
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Old   August 2, 2010, 16:50
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I assume you are referring to a condition on the third derivative of the function to be solved for - in that case the answer is yes - it is incorrect. You would specify conditions on the function or the derivative of the function (or a mixture). The differential equation itself only defines the nth derivative of the function, so n+1 order derivative information on the boundaries is really meaningless.

If you are referring to the order of accuracy of a discretization scheme, then the statement makes sense mathematically, since you could have a third-order accurate approximation to a first-derivative. But it may or may not adversely interact with the 2nd-order approximation of the interior scheme.
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Old   May 6, 2015, 16:19
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Thanks a lot for the explanation.
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