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Numerical Methods by Babu Ram

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11

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

 

Auxx + Buxy + Cuyy + Dux + Euy+ Fu = G,

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:

  1. 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.
  2. If B

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