Apply gauss’s forward formula to find the value of u9 if u0=14, u4=24, u8=32, u12= 35, u16= 40

Sol:-       x = a + uh

              9 = 8 + u(4)

             u = 9 – 8   =   1  = 0.25

                    4           4

             [u = 0.25]

u    x    f(x)   ∆f(x)    ∆²f(x)     ∆³f(x)    ∆⁴f(x)

-2  0    14

                     10

-1  4    24                   -2

                      8                          -3

0   8    32                    -5                          10

                      3                           7

1  12   35                     2

                      5

2  16   40

F(u) = 3.2 + 0.25 + 0.25(0.25 – 1)                           

                      1              2

+ 0.25(0.25 – 1)(0.25 + 1) (7)

              3 × 2

+ 0.25(0.25 – 1)(0.25 + 1) (0.25 – 2)  (10)

                4 × 3 × 2

f(u) = 32 + 0.75 + 0.46875 + (-0.2734375)  + 0.17089

       = 33.1162025