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

... ∇ and 4 log 50 = 0.0508 ∇−Example 10. Given that:123456781 8 27 64 125 216 343 512xyConstruct backward difference table and obtain 4 ()f8∇.108 COMPUTER BASED NUMERICAL AND STATISTICAL ... 22()dfxdx 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 of mutually dependent quantities ... Difference Operators (a) The Operator E: The operator E is called shift operator or displacement or translationoperator. It shows the operation of increasing the argument value x by its interval of differencingh...

A textbook of Computer Based Numerical and Statiscal Techniques part 62 docx

... the RangeLower limit a = 0Upper limit b = 6Enter the number of subintervals = 6Value of the integral is: 1.3571598 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Enter the value of y2 ... ALGORITHM FOR TRAPEZOIDAL RULEStep 1. Start of the program for numerical integrationStep 2. Input the upper and lower limits a and bStep 3. Obtain the number of subinterval by h = (b a) /nStep 4. ... RULE#include<stdio.h>#include<conio.h>float sim(float);void main(){float res, a, b, h, sum;int i, j, n;600 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Step 13. temp = 1/ (1+(x * x))Step 14. Return tempStep 15. End of...

A textbook of Computer Based Numerical and Statiscal Techniques part 8 doc

... 1.79630762 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES 2.6.2 Rate of Convergence of Iteration MethodLet f(x) = 0 be the equation which is being expressed as x = g(x). The iterative formula for ... (0.6072) + 1] = 0.6071Now, x5 and x6 being almost same. Hence the required root is given by 0.607.56 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES First approximation: 1020 01) 0()(()xxxx ... 3.78863ALGEBRAIC AND TRANSCENDENTAL EQUATION65Example 5. Find the real root of equation f(x) = x3 + x2 – 1 = 0 by using iteration method.Sol. Here, f(0)= – 1 and f(1) = 1 so a root lies...

A textbook of Computer Based Numerical and Statiscal Techniques part 9 docx

... 66 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Putting i = 2 in (1) x3 = 0.02439Therefore reciprocal of 41 is 0.0244.Example 8. Find the square root of 20 correct to 3 decimal places ... x2 = x3 up to four decimal places. So we have 12 = 3.4641.72 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES = ()()100.4343 2. 8133 1.22.4128log 2. 8133 0.4343 0.8835+=+or ... 0.607168 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES From which we have, h = – ()()00fxfx′, where [f ′(x0)¹ 0].Hence, if x0 be the initial approximation, then next (or first) approximation...

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

... 12.Similarly we have obtained ∆3u0 = 6 and ∆4u0, ∆5u0 , are all zero as ur = r3 is a polynomial of third degree. 130 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES PROBLEM ... ax−−−=0!nnnhax= !nnnha 132 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Hence, we have nth difference of the polynomial is constant and so all higher differences areeach zero. i.e.12() ... functional values:Sol.12345672 5 10 18 26 37 50xy 134 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES From this table we have the third differences are quite iregular and the irregularity...

A textbook of Computer Based Numerical and Statiscal Techniques part 21 docx

... = 0.047875190 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 4. Use Gauss’s forward formula to find a polynomial of degree four which takes thefollowing values of the function ... No. of Persons earning wages between Rs. 60 to 70 is 423.59375 – 370 = 53.59375 or54000. (Approx.)186 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Take the mean of equation (1) and (2)22(0) ... formula to find the value of U9, ifu(0) = 14, u(4) = 24, u(8) = 32, u (12) = 35, u(16) = 40 [Ans. 33.1162109]192 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES 5. Apply Gauss forward formula...

A textbook of Computer Based Numerical and Statiscal Techniques part 31 docx

... DIFFERENTIATIONThe 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 ... Newtonforward formula, and if the same is required at a point near the end of the set of given tabular294INTERPOLATION WITH UNEQUAL INTERVAL289Example 1. Obtain cubic spline for every subinterval, ... + NUMERICAL DIFFERENTIATION AND INTEGRATION295values, then we use Newton’s backward interpolation formula. The central difference formula(Bessel’s and Stirling’s) used to calculate value...

A textbook of Computer Based Numerical and Statiscal Techniques part 34 docx

... +6(0.3777)]316 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES 6.5 TRAPEZOIDAL RULEPutting n =1 in equation (2) and taking the curve y = f(x) through (x0, y0) and (x0, y0) as a polynomial of ... 1.366173 413. Ans.324 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 6. Evaluate the integral 6301dxx+∫by using Weddle’s rule.Sol. Divide the interval [0,6] into 6 equal parts each ... known as Simpson’s one-third rule.Note: Using the formula, the given interval of integration must be divided into an even number of sub-intervals.320 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Sol....

A textbook of Computer Based Numerical and Statiscal Techniques part 36 docx

... approximation of the error, we have. 13 21829515x ≤ .00005.Taking logarithm, we obtain 15 log x ≤ log .00005 218295 13 afa for x ≤ .988.340 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example ... integrate.Thus, when, ()10.1, 1 0.1 2log 1.1 0.9828xy==−+ =. Ans.Here in this example, only I approximation can be obtained and so it gives that approximatevalue of y for 0.1x=Example ... nnyyhfxy+=+342 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Thus, xxx371136322079++ represents y correct to 4 decimal places. In the range |x| ≤ .988.i.e. –0.988 ≤ x ≤ 0.988.Example 13. ...

A textbook of Computer Based Numerical and Statiscal Techniques part 37 doc

... Using Picard’d method, obtain the solution of ()()31;03dyxxyydx=+ = 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,,xyzby ()111,,xyz in the above formulae.350 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Since, () ()34111.039473,yy== correct to 6 decimal placesHence, ... +1.0082=352 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES 6. Solve the following initial value problem by Picard methodydyxedx= with ()00y=, compute ()0.1y.[Ans. 0.0050125]7. Use Picard’s...

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