Numerical Methods old question papers

• a) Solve xlog,,x=1.2by Newton- Raphson method correct to four decimal places.
• b) — Using Secant Method, find the roots of function 2x — logigx-7=0 Correct up to three decimal places.

OR

Find the root of the equation f(x) = x?-4x-10 correct to three decimal places by using False Position method.

• a) From the following data given in the table below evaluate f (2.5) by using Lagrange method. L414 | 1.732
• b) From the following table, Estimate the number of student who obtained marks between 50 and 55, 30-40 | 40-50 | 50-60 | 60-70 | 70-80 No of Sade

• a) Compute the Simpson’s 1/3 and Simpson’s 3/8 rule for | = ik edx using a regular partition with subinterval n=6.
• b) Use the Romberg integration to find the solution correct upto three decimal places. 1 i=/ ~ J 14x? 0 3

3x+-y+z=10

• a) Solve: 2x+3y+2z=14 x+2y+3z=14 By Gauss elimination method.
• b) Solve the following system of equations using Crout method. xtyt+z= 4x+4y74+3z=8,x+6y+2z=6

OR

Find largest eigen value and corresponding eigen vector of the matrix. 3 -l 2 4 -3 0 -1

• a) Solve the following differential equation within 0<x<0.3 using RK-4™ order Method. d 102 =x? + y2,y(0) =1withh = 0.1
• b) Apply Euler’s method to approximate value of y(0.3) for the differential equation: = =y+xy(0) =1.

• a) For square bar of size 1Scmx15cm, calculate the steady state temperature at interior point for the grid size of SemxScm. orc oc P|. 100°C oc Ld. 100°C 100°C
• b) Solve the Poisson equation W7f=2x"+ y, over the square domain 1<x <A, 1<y <4, with f=0 on the boundary. Take step size in x and y, h=k=1.

Write short notes on: (Any two) 2x5

• a) Errors in Numerical Method
• b) __Ill-conditioned systems