We will derive the finite difference approximations for and .

Let

denotes and respectively

and

.

We prove that

[1]

Let , Taylor series

is

i.e.,

Hence,

[2]

Let , Taylor series

becomes

It follows that

Similarly, let ,

Since , we have

(1)-(2)

Therefore,

[3]

Let , Taylor series

becomes

.

That is,

Similarly, let , we have

.

i.e.,

(3) + (4)

.

Therefore,