SRM University 2008 B.Tech Electrical and Electronics Engineering NUICAL METHODS - Question Paper

B.Tech(PT)DEGREE EXAMINATION,DECEMBER 2008
2nd Semester
PMA202-NUMERICAL METHODS
Time:3 Hours Max.marks:100
ans ALL ques.
PART-A(10*2=20 Marks)


1.State principle of lowest squares.

2.Write down Newton Raphson formula.

3.Define the operators :(i)d (ii)µ.

4.Give the Newton’s divided difference interpolation formula..

5.Write th e numerical integration formula using trapezoidal method.
four
6.Evaluate ? e^x dx,using simpson’s 1/3rd rule.
0
eº = 1,e¹ = 2.72,e² =7.39,e³ = 20.09,e^4 =54.6.

7.State Taylor’s algorithm for the 1st order differential formula.

8.How many prior values are needed to predict the next value in milne’s method?

9.Classify the PDE xUxx + yYyy =0, x > 0,y > 0.

10.Write the crank-nicholson difference scheme to solve Uxx = aUt with u(0,t) = t0, u(l,t)=t1, , u(x,0)= f(x).


PART-B(5*16 = 80Marks)
11.a.Fit a parabola to the subsequent data:
x 1 2 3 4 5
y 2 3 5 8 10


(OR)
b.Solve by Gauss jacobi method
12x +4y-z =32
x +3y+10z = 24
2x +17y+4z =35

12.a. Apply Newton’s backward difference formula to the data beneath toobtain a polynomial of degree 4.

x 1 2 3 4 5
y 1 -1 1 -1 1



(OR)
b. Use Lagrange’s formula to obtain x when y = 85 from the following:

x 2 5 8 14
y 94.8 87.9 81.3 68.7

13.a.Find ƒ'(x) and ƒ''(x) at x = 1.1.Given
x 1 1.1 1.2 1.3 1.4 1.5 1.6
y 7.9 8.4 8.7 9.1 9.4 9.7 10.1

six (OR)
b.Evaluate ? dx/1+x² using (i) simpson’s 1/3 rule (ii) simpson’s 3/8 ruleand compare the outcome with
0
the exact integration.
14.a.Solve the formula dy/dx = 1- y with x =0,y = 0 using replaced Euler method.Find y(0.1), y(0.2).
(OR)
b.Using Milne’s predictor and corrector formula,find y(4.4) provided
5xy' + y² =2,y(4) =1, y(4.1) =1.0049, y(4.2) =1.0097 and y(4.3) =1.0143.

15.a. Solve Uxx +Uyy = 0 over the squre mesh of side four units, satisfying the subsequent boundary conditions.
(i) u(0,y) = 0 for 0 = y = 4
(ii) u(4,y) = 12+y for 0 = y = 4
(iii) u(x,0) = 3x for 0 = x = 4
(iv) u(x,4) = x² for 0 =x = 4

(OR)
b.Solve the formula Ut = Uxx subject to the conditions u(x,0) = sin px, 0 =x = 1, u(0,t) = u(1,t) =0
using crank Nicholson method.

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Earning:   Approval pending.