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
*B*^{2}– 4*AC*<; 0 at a point in the (*x*,*y*) plane, then the equation is called elliptic. For example, the equation*u*_{xx}+*u*_{yy}= 0, known as Laplace equation, is elliptic. - If
*B*

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