Answer to Question #118371 in Quantitative Methods for sarthak garg

Question #118371
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
1
Expert's answer
2020-05-28T18:35:00-0400

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


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