×

Close

- Numerical Methods - NM
- 2017
- PYQ
**Biju Patnaik University of Technology Rourkela Odisha - BPUT**- Electrical and Electronics Engineering
- B.Tech
**1542 Views**- 19 Offline Downloads
- Uploaded 1 year ago

Registration No: Total Number of Pages: 02 B. Tech. FESM6301 5th Semester Back Examination 2017-18 Numerical Methods BRANCH : EEE, ELECTRICAL, MINERAL, MINING Time: 3 Hours Max Marks: 70 Q.CODE: B155 Answer Question No.1 which is compulsory and any five from the rest. The figures in the right hand margin indicate marks. Q1 g) h) i) j) Answer the following questions: Round off the number 435.235 to four significant digits and then calculate relative error. What is the difference between relative error and approximate error ? State the order of convergence and convergence condition for fixed point iteration method. Define order of an iterative method. What is the order of Secant Method ? What is the condition of convergence of Gauss Seidel Method ? Write the divided difference table for the data given below : X 1 2 4 7 Y(x) 22 30 82 106 Define natural spline function. Explain multistep method giving suitable example. State eigen value problem. Write the error in Euler’s Method. Q2 a) b) Find the root of equation Find a positive root of = Q3 a) a) b) c) d) e) f) − = 0 using Newton Raphson method. + by using Secant Method. Q4 a) b) Q5 Q6 if A = − Solve the following system of equations by using Gauss Seidel method : 4x + y +2 z = 4; 3x + 5y + z = 7; x + y +3z = 3 Using Newton’s Divided Difference formula, find the value of f(0.5) and f(3.5)given the following table X -2 0 1 4 F(x) -23 1 4 82 Obtain cubic spline approximation for the function defined by the data X 0 1 2 3 Y 1 2 33 244 a) Evaluate = ∫ eight equal parts. b) Using Romberg Integration, evaluate a) Solve the IVP = + , ( ) = interval [0,0.2] Find the value of (0.2)of the IVP 4th order. b) (5) (5) (5) By Gaussian Elimination, find b) (2 x 10) using Simpson’s 1/3rd rule dividing the interval into = ∫ + , ( )= (5) (5) (5) (5) . using Modified Euler’s Method in the = (5) using Rungekutta (5) (5)

Q7 Using power method, find all the Eigen values of the following matrix : (10) Q8 Using shooting method , solve 7y”-2y’-y +x=0 with boundary conditions (0) = 5 & (20) = 8 (10)

## Leave your Comments