Elementary Finite Difference Quotients

In order to obtain a finite difference for the second-order partial derivative add Eq. (2.1) and 2.5). This produces

(2.9)

Solving Eq. (2.9) for we obtain

(2.10)

Eq. (2.10) is a second-order central difference form for the derivative at grid point

Difference quotients for the derivatives are obtained in exactly the similar way. The results are analogous to the expression for the derivatives.

	[Forward difference]
	[Backward difference]
	[Central difference]
	[Central difference of second derivative]