Order of standard scheme

Minimum number of

grid points required

(k = n + 1)

Number of

possible standard schemes when

Number of

possible standard schemes when, and j = 1 is a grid point

First-order (n = 1)

2

C(5,2) = 10

C(1,1).C(4,1) = 4

Second-order (n = 2)

3

C(5,3) = 10

C(1,1).C(4,2) = 6

Third-order (n = 3)

4

C(5,4) = 5

C(1,1).C(4,3) = 4

Fourth order (n = 4)

5

C(5,5) = 1

C(1,1).C(4,4) = 1