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for example, the equaiton governing the dynamic behavior of a 1D bar is:

[itex] \frac{\partial ^{2}u}{\partial x^2} = \frac{1}{c^2} \frac{\partial ^{2}u}{\partial t^2} [/itex]

the maximum order of the essential boundary condition is 0 :

[itex] u(0,t)=0[/itex]

and the maximal order of the natural boundary condition is 1:

[itex] EA\frac{\partial u}{\partial x}(L,t)=R(t) [/itex]