A textbook of Computer Based Numerical and Statiscal Techniques part 13 doc

... ∇ and 4 log 50 = 0.0508 ∇− Example 10. Given that: 12345678 1 8 27 64 125 216 343 512 x y Construct backward difference table and obtain 4 () f8∇ . 108 COMPUTER BASED NUMERICAL AND STATISTICAL ... 2 2 () d fx dx and so on. The operator ∆ is an analogous to the operator D of differential calculus. In finite differences, we deal with ratio of simultaneous increments o...

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... the Range Lower limit a = 0 Upper limit b = 6 Enter the number of subintervals = 6 Value of the integral is: 1.3571 598 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Enter the value of y2 ... ALGORITHM FOR TRAPEZOIDAL RULE Step 1. Start of the program for numerical integration Step 2. Input the upper and lower limits a and b Step 3. Obtain the number of sub...

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... 1.796307 62 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES 2.6.2 Rate of Convergence of Iteration Method Let f(x) = 0 be the equation which is being expressed as x = g(x). The iterative formula for ... (0.6072) + 1] = 0.6071 Now, x 5 and x 6 being almost same. Hence the required root is given by 0.607. 56 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Fir...

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... 66 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Putting i = 2 in (1) x 3 = 0.02439 Therefore reciprocal of 41 is 0.0244. Example 8. Find the square root of 20 correct to 3 decimal places ... x 2 = x 3 up to four decimal places. So we have 1 2 = 3.4641. 72 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES = () () 10 0.4343 2. 8133 1.2 2.4128 log 2. 8133 0...

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... 12. Similarly we have obtained ∆ 3 u 0 = 6 and ∆ 4 u 0, ∆ 5 u 0 , are all zero as u r = r 3 is a polynomial of third degree. 130 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES PROBLEM ... ax − −− = 0 ! n n nhax = ! n n nha 132 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Hence, we have nth difference of the polynomial is constant and so...

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... = 0.047875 190 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 4. Use Gauss’s forward formula to find a polynomial of degree four which takes the following values of the function ... No. of Persons earning wages between Rs. 60 to 70 is 423.59375 – 370 = 53.59375 or 54000. (Approx.) 186 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Take the mean o...

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... DIFFERENTIATION The method of obtaining the derivatives of a function using a numerical technique is known as numerical differentiation. There are essentially two situations where numerical differentiation ... Newton forward formula, and if the same is required at a point near the end of the set of given tabular 294 INTERPOLATION WITH UNEQUAL INTERVAL 289 Example 1. Obta...

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... +6(0.3777)] 316 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES 6.5 TRAPEZOIDAL RULE Putting n =1 in equation (2) and taking the curve y = f(x) through (x 0 , y 0 ) and (x 0 , y 0 ) as a polynomial of ... 1.366173 413. Ans. 324 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 6. Evaluate the integral 6 3 0 1 dx x+ ∫ by using Weddle’s rule. Sol. Divi...

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... approximation of the error, we have. 13 218295 15 x ≤ .00005. Taking logarithm, we obtain 15 log x ≤ log .00005 218295 13 afa f or x ≤ .988. 340 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example ... integrate. Thus, when, () 1 0.1, 1 0.1 2log 1.1 0.9828 xy ==−+ = . Ans. Here in this example, only I approximation can be obtained and so it gives that approximate...

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... Using Picard’d method, obtain the solution of () () 3 1;03 dy xxyy dx =+ = Compute the value of () 0.1y and () 0.2y .[Ans. 3.005, 3.020] 348 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Now, ... simply replace () 000 ,, xyz by () 111 ,, xyz in the above formulae. 350 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Since, () () 34 11 1.039473, yy==...

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