TAILIEUCHUNG - A textbook of Computer Based Numerical and Statiscal Techniques part 8

A textbook of Computer Based Numerical and Statiscal Techniques part 8. 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. | 56 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES First approximation X1 - xo x2 x0 J x0 f x1 - f xo 1 - 15 1 1 7 1 014085 Now f x2 f - 3 - 3 - . Thus the root lies between and . Then taking x0 x1 f x0 - and f x1 . Second approximation The next approximation to the root is Now x3 x0 - 1 0 f x0 3 0 f x1 - f x0 - 1 7 00396 f x3 f 0456 - 3 - 3 . Thus the root lies between and . Then taking x0 x1 f x0 and f x1 . Third approximation The next approximation to the root is Now 1 - x0 x4 x0 J x0 f x1 - f x0 . nnnrn. 1 0456 - 3 7225 0 0252 -0 0252 10456 0 0115 f x4 f g1 0487 - 3 - 3 - Thus the root lies between and . Fourth approximation Taking x0 x1 f x0 - and f x1 . Then the root becomes 1 - x0 15 x - f x - 0 f x0 ALGEBRAIC AND TRANSCENDENTAL EQUATION 57 - . Now f 5 f e1-0496 - 3 - 3 - . Thus the root lies between and . Fifth approximation Taking x0 x1 f x0 - and f x1 . Then the next approximation to the root is given by x6 X0 - x1 - x0 f x1 - f x0 f X0 . Hence the root is approximately correct to three decimal places. Example 6. Find a real root of the equation x2 - loge x - 12 0 using Regula-Falsi method correct to three places of decimals. Sol. Let f x x2 - loge x - 12 0 So that f 3 32 - loge 3 - 12 - and f 4 42 - loge 4 - 12 and Therefore f 3 and f 4 are of opposite signs. Therefore a real root lies between 3 and 4. For the approximation to the root taking x0 3 x1 4 f x0 - and f x1 . First approximation By Regula-Falsi .

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