Page 229 - Engineering Mathematics Workbook_Final

Numerical Methods

FORWARD DIFFERENCE OPERATOR (a) 1 (b) 2

113. The values of a function f(x) are (c) 3 (d) 4
tabulated below
[GATE-2017 (IN)]
x 0 1 2 3
f(x) 1 2 1 10
Using Newton’s forward difference
formula, the cubic polynomial that
can be fitted to the above data, is

3
2
2
(a) 2x + 7x − 6x +
(b) 2x − 7x + 6x −
2
3
2
3
2
(c) x − 7x − 6x + 1
3
2
(d) 2x − 7x + 6x + 1
[GATE-2004]

114. The following table lists an nth order
polynomial
+
+
n
f ( ) x = a x + a x n− 1 + ..... a x a 0
n−
1
n
1
and the forward differences
evaluated at equally spaced values of
x. The order of the polynomial is
x f(x) f   2 f  3 f

-
-0.4 1.7648 0.089 -0.03
0.2965
- -
-0.3 1.4683 0.059
0.2075 0.0228
- -
-0.2 1.2608 0.0362
0.1485 0.0156
- -
-0.1 1.1123 0.0206
0.1123 0.0084
- -
0 1 0.0122
0.0917 0.0012
-
0.1 0.9083 0.011 0.006
0.0795

0.2 0.8288 0.0685 0.017 0.0132

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