×

Close

- Numerical Methods - NM
- 2017
- PYQ
**Biju Patnaik University of Technology Rourkela Odisha - BPUT**- Electronics and Instrumentation Engineering
- B.Tech
**1886 Views**- 19 Offline Downloads
- Uploaded 2 years ago

Registration no: Total Number of Pages: 02 B.Tech. PEI5H001 5th Semester Regular Examination 2017-18 Numerical Methods BRANCH : AEIE, EIE, IEE Time: 3 Hours Max Marks: 100 Q.CODE: B388 Answer Question No.1 and 2 which are compulsory and any four from the rest. The figures in the right hand margin indicate marks. Q1 a) b) c) d) Answer the following questions: Fill in the Blanks : The order of convergence in Regula falsi method is ----------------. Newton –Raphson formula to find a root of f(x)=0 is---------------. For a cubic polynomial which takes the following values (0) = 1, (1)0, (2) = 1, (3) = 10,then (4) = − − − −. By Trapezoidal rule, taking n=4, the value of ∫ is-------------------. e) The value of √12 correct to three decimal places by Newton-Raphson Method is ------------------. f) g) h) The Taylor’s series for log (1 + ) is-------------------. Newton’s backward difference interpolating polynomial is---------------------. 4 2 The largest eigen value of of the matrix is------------------. 1 3 The error in Simpson’s rd rule is-------------------. i) j) The approximate value of ∫ √cos dx is----------------------. a) b) c) d) e) What is propagation of error and approximate error? What is the condition of convergence of fixed point iteration method? Explain geometrical interpretation of secant method. Explain Gauss –Siedel iteration method. If = , find[1,2,3,4]. Explain Newton’s divided difference interpolation. Explain Trapezoidal rule. How Modified Euler’s Method is different from Euler’s method. Write the formula Mine’s method to solve the I V P = ( , ), ( ) = . (2x10) (2×10) Q2 f) g) h) i) Q3 j) Find ∆ 2 , ∆ being Newton’s Forward difference operator. a) Using Regula-falsi method find a real root of − − 12 = 0 correct up to three decimal places. Find the root of + ln − 2 = 0 in (1,2) by fixed point iteration method. (7.5) Solve the following system of equations by LU decomposition method. 2 −3 +4 = 8 + + 4 = 15 3 +4 − = 8 (7.5) b) Q4 a) (7.5)

Q5 Q6 Q7 + 8 +4 = 9 − 3 + 2 = 20 4 + 11 − = 33 by Gauss- Siedal iteration method. b) Solve the system a) Find f(8) using following data by Lagrange’s Method: x 4 5 f(x) 48 100 (7.5) (7.5) 7 294 10 900 11 1210 b) Construct Newton’s forward difference polynomial for the following data x 0 1 2 3 f(x) 1 2 1 10 Hence evaluate f(1.5) (7.5) a) (7.5) b) Evaluate∫ using Romberg’s method correct upto 4 decimal places and hence find approximate value of . Evaluate = ∫ cos using Gauss two point and three point rule. a) Evaluate by Modified Euler’s method b) Using R-K method of fourth order, find y(0.2),given + = , (1) = 1, = (7.5) = 1.3 , (0) = 1 at (7.5) = 0.2 (7.5) Taking h=0.1 Q8 a) b) Using Adam -Bashforth method, find y(0.4) ,given that ′ = 1 + , (0) = 2. Using Taylor’s series method obtain the values of ‘ ’ at = 0.2 correct to four decimal Places if satisfies the equation " = ,given that ′ = 1 and = 1 when = 0. (7.5) (7.5) Q9 a) b) Explain cubic spline interpolation Derive Newton-cote’s Rule of numerical integration. (7.5) (7.5)

## Leave your Comments