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Order of boundary conditions in a Partial Differential Equation |
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August 2, 2010, 16:28 |
Order of boundary conditions in a Partial Differential Equation
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#1 |
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Gaurav
Join Date: Aug 2010
Location: London
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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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August 2, 2010, 17:50 |
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#2 |
Senior Member
Join Date: Jul 2009
Posts: 358
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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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May 6, 2015, 17:19 |
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#3 |
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Gaurav
Join Date: Aug 2010
Location: London
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Thanks a lot for the explanation.
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boundary conditions, mathematics, pde |
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