Answer to Question #118371 in Quantitative Methods for sarthak garg

Question

Using Bessel’s difference interpolation formula, to compute the value of y(5) for the
following data given below:
x: 0 4 8 12
y: 14.27 15.81 17.72 19.96

Answer 1

x_-1=0 y_-1=14.27 dy_-1=y₀-y_-1=1.54 d²y₁=dy₀-dy-₁=0.37 d³y₁=-0.04

x₀=4 y₀=15.81 dy₀=y₁-y₀=1.91 d²y₂=dy₁-dy₀=0.33

x₁=8 y₁=17.72 dy₁=y₂-y₁=2.24

x₂=12 y₂=19.96

x₀=4,h=5

u=(5-4/4)=0.25

f(5)=(y₀+y₁)/2+(u-1/2)dy₀+(u(u-1))/2!*(d²y₁+d²y₂)/2+(u*(u²-u))/3!*d³y₁=((17.72+15.81)/2+0.25*1.91)+(((0.25)²-0.25)/2!*(0.37+0.33)/2)+((0.25*((0.25)²-0.25)/3!)*(-0.04))=17.2425--0.0328125+0.0003125=17.275625