Order of boundary conditions in a Partial Differential Equation

gaurav_bhutani · August 2, 2010, 15:28

Is it mathematically incorrect to have a 3rd order boundary condition for a 2nd order Partial Differential Equation?

agd · August 2, 2010, 16:50

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.

gaurav_bhutani · May 6, 2015, 16:19

Thanks a lot for the explanation.

August 2, 2010, 15:28	Order of boundary conditions in a Partial Differential Equation	#1
gaurav_bhutani New Member Gaurav Join Date: Aug 2010 Location: London Posts: 5 Rep Power: 15	Is it mathematically incorrect to have a 3rd order boundary condition for a 2nd order Partial Differential Equation?

August 2, 2010, 16:50		#2
agd Senior Member Join Date: Jul 2009 Posts: 351 Rep Power: 18	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. gaurav_bhutani likes this.

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May 6, 2015, 16:19		#3
gaurav_bhutani New Member Gaurav Join Date: Aug 2010 Location: London Posts: 5 Rep Power: 15	Thanks a lot for the explanation.