Numerical Analysis
Assignment No. 2
Due Date: 12 April 2012
Q No. 1: Suppose a table is to be prepared for the function f(x) = sin(ln x) with 2.0≤x≤2.6.
If the number of decimal places to be given each entry is d≥5 and that the difference between
x-values i-e; the step size is h. What should be the value of hfor linear lagrange polynomial
to give an absolute error of atmost 10−5. Use this value of hto interpolate f(2.3) by using
linear lagrange polynomial and compare your result.
Q No:2 Form a difference table for the function given below. Find the values of a, b, c so that
44f(a) = ∇4f(b) = δ4f(c) = −0.0428.
x0123456
f(x) .3679 .7358 .9197 .9810 .9963 .9994 .9999
Q No: 3 Show that δ2=4−∇=4∇ − ∇4 where δ, 4,∇are central, forward and backward
difference operators respectively.
Q No: 4 You measure the voltage drop v, for a number of different values of current ias:
i0.25 0.75 1.25 1.75 2.25
v-0.23 -0.33 0.70 1.88 6.00
Use a suitable interpolation formula to estimate the voltage drop for i= 0.9Amp.
School of Electrical Engineering and Computer Sciences, National University of Sciences and Technology, Islamabad,
Pakistan.
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