Numerical Methods PU Spring question paper

• a) The following table gives the displacement, x(cms.) of an object at various time, t(seconds). Find the displacement of this object at t=1.3 second and t=1.5 second, using any suitable interpolation formula. ae
• b) The growth of bacteria(N) in a culture after t hours is given by the following table: i If the relationship between bacteria N and time t is of the form N=ab‘.Using least square approximation estimate the N at t =5 hr. zi 3 ex °

• a) Find S dx by using: an i. Trapezoidal rule
• ii) Simpson’s 1/3 rule
• iii) Simpson’s 3/8 rule
• b) Use the Romberg integration to find the solution correct upto three decimal places. ray f= fy 1+x?2 a 7 “if using

sy ela 38 SH LLDY

• a) Find the inverse of the square matrix, A [: -2 Gauss-Jordan elimination method. 5 : ‘ : i uation using
• b) Find the solution of the given simultancous linear eq Gauss Seidel method. 6x—2y+z=11 -2x+7y+2z=5 x+2y—-5z=-1 within 0<x<0.5 using Rk 4"

• a) _ solve the following differential equation within 0<x<0.5 using order method 10d? y/dx?+2dy/dx-3y=5, y(0)=0,y'(0)=0. femsneees
• b) Using the Euler's (R-KI & order method) find an approximate value ¢ of y corresponding to x=1, given that dy/dx = X+¥ and y= 1. When x=0, h=0.1.

• a) Torsion on a square bar of size 15cm * 15cm. If two of the sides are held at 100°C and the other two sides are held at 0°C. Calculate the steady state temperature at interior points. Assume a grid size of Sem x Sem.
• b) Solve the Poisson equation W7f=2x"+ y, over the square domain 1<x <A, 1<y <A, with £0 on the boundary. Take step size in x and y, h=k=1.

Write short notes on: (Any two) 2x5

• a) Applications of Numerical Methods in Engineering
• b) Error in Numerical Method
• c) Ill condition and well-conditioned system (teas X\ ws