tailieunhanh - A textbook of Computer Based Numerical and Statiscal Techniques part 23

A textbook of Computer Based Numerical and Statiscal Techniques part 23. 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. | 206 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES 7. Apply Stirling s formula to find a polynomial of degree four which takes the values of y as given below x i 2 3 4 5 y i -1 1 -1 1 Ans. u4 - 8 u2 1 3 3 8. Apply Stirling s formula to interpolate the value of y at x from the following data x y Ans. BESSEL S Example 1. Using Bessel s formula find the value of y at x for the data given below x y Sol. Difference table for the given data is as x y A A2 A3 A4 A5 -2 -1 0 1 2 3 Here h x - a _ - u h . INTERPOLATION WITH EQUAL INTERVAL 207 Now from Bessel s formula we have f u f 0 f 1 2 1 u - 2jAf 0 u u -1 a2f 0 A2f -1 2 2 L 1Ï u u 1 I u -------. A3 f -1 u 1 u u 1 u 2 A4 f 1 A4 f 2 4 2 u 1 u u 1 u 2 u 1 2 5 A5 f 2 . 1 2 05 x 1 0 1 x 16 9 2 0 . Approx. Example 2. Following table gives the values of ex for certain equidistant values of x. Find the value of ex at x using Bessel s formula x ex Sol. Given h take it origin as x a _ _ h u Difference table for the given data is as x f x A A2 A3 A 4 A 5 A6 0 208 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Bessel s formula f u f 0 f 1 u - 1 Af 0 u u-1 iA2f 0 A2f -1 . 2 A3 f 11 TI 2 f 3 A f -1 u 1 u u- 1 u-2 f A4 f -1