Partial Differential Equations
Partial differential equations appear in the description of physical processes in applied sciences and engineering. A differential equation that involves more than one independent variable is called a partial differential equation. We restrict ourselves to second order partial differential equations. The general second order linear partial differential equation is of the form
where A, B, C, D, E, F, G are all functions of x and y. Equations of the above form can be classified into three types:
- If B2 – 4AC <; 0 at a point in the (x, y) plane, then the equation is called elliptic. For example, the equation uxx + uyy = 0, known as Laplace equation, is elliptic.
- If B