A textbook of Computer Based Numerical and Statiscal Techniques part 15 doc

... 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 a...

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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 ... 0.6071 68 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES From which we have, h = – () () 0 0 fx fx ′ , where [f ′(x 0 )¹ 0]. Hence, if x 0 be the initial approximati...

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... ∇ 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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... = 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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... 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. Divide the interval [0,6] into 6 equal parts each of ... 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...

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... 218295 13 afa f or x ≤ .988. 340 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 10. Obtain y when x = 0.1, x = 0.2 Given that ; dy xy dx =+ y(0) = 1, Check the result with exact value. Sol. ... to 4 decimal places, then using the first neglected term, namely 13 218295 15 x as an approximation of the error, we have. 13 218295 15 x ≤ .00005. Taking logarithm,...

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... () () 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, using Euler’s modified formula, we obtain () ()()()( ) 221 2 0.1 .828 ... simply replace () 000 ,, xyz by () 111 ,, xyz in the above formulae. 350 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Since, () ()...

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