Odd order governing equation - FE formulation
We generally encounter governing equations of even order. In FE formulation we get a symmetric coefficient matrix 'A' (AX = B). I have a few doubts as follwing.
[a] Any odd order governig equations ? If so, you may please write.
[b] Say, it has a functional also, then, what's the order of that differentiation?
[c] For even order (n) differential equations (DE), when we use weak formulation approach, we bring down the order to n/2. This finally gives us a symmetric coefficients matrix 'A' (weighting function and shape function are same). But, for odd order DE, when weak formulation is used, then, what's the reduction in the order. I think it may not be n/2.
You may plese throw some light on the above questions.