tailieunhanh - A textbook of Computer Based Numerical and Statiscal Techniques part 24

A textbook of Computer Based Numerical and Statiscal Techniques part 24. By joining statistical analysis with computer-based numerical methods, this book bridges the gap between theory and practice with software-based examples, flow charts, and applications. Designed for engineering students as well as practicing engineers and scientists, the book has numerous examples with in-text solutions. | 216 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Difference table is u f u Af u A2f u A3 f u -1 2854 308 0 3162 3926 3618 -6648 1 7088 896 -3030 2 7984 By Everett s formula f .25 7088 125 X-075 -3030 . 3162 -25 3618 .1 I 3 JI 5 J 4064 Hence f 30 4064. Example 3. Apply Laplace Everett s formula to find the value of log 2375from the data given below x 21 22 23 24 25 26 log x Sol. Here h 1 We take origin at 23. Now difference table is given by x log x A A2 A3 A4 A5 -2 21 -1 22 0 23 0 1 24 2 25 3 26 INTERPOLATION WITH EQUAL INTERVAL 217 Here h 1 . u x-a 23-75 - 23 h 1 w 1 - From Laplace Everett formula we have f u Lf 1 1 -1 A2 f 0 2 u 1 u u- 1 u - 2 A4 f -1 .1 3 5 Lf 0 W 1 W W -1 A 2 f -1 w 2 w 1 w w - 1 w - 2 A 4 f -2 I z 5025 x L75 M0 -025 -1-25 x 58 5 x 1 6 120 _ log 2375 log x 100 log log 100 log 2375 2 Example 4. Find the value of ex when x from the following data x e x Sol. Here h take origin as . The difference table for the given data is as x e x A A2 A3 A 4 A 5 218 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES u 1748 -174 w f 1 8 062 x 0i2 o x - . Example 5. Prove that if third differences are assumed to be constant yx xy1 A2y0 uy0 31 A2y-1 where u 1 - x. .