Question

The classification of PDEs are governed by ________

(a) Their highest order derivatives

(b) Their least order derivatives

(c) The number of terms

(d) The constants

The question was asked at a job interview.

I need to ask this question from Classification of PDE in chapter Mathematical Behaviour of Partial Differential Equations of Computational Fluid Dynamics

Answer 1

Right answer is (a) Their highest order derivatives

To elaborate: The highest order derivatives of a PDE determines its type. Only the coefficients A, B and C are used to find the type of A\(\frac{\partial^2 \Phi}{\partial x^2}+B\frac{\partial ^2 \Phi}{\partial x\partial y}+C\frac{\partial^2 \Phi}{\partial y^2}+D\frac{\partial \Phi}{\partial x}+E\frac{\partial\Phi}{\partial y}+F\Phi +G=0\).