Numerical Methods PU Spring 2023 question paper

• a) Explain in brief the errors in numerical calculations. 5.
• b) Find a root of 3x+sinx-e* =0 using
• i) One of the bracketing methods and
• ii) | One of the non-bracketing methods

• a) From the data given below, find the number of students whose weight is between 60 to 70. Weight in 0-40 40-60 | 60-80 | 80-100 | 100-120 Ibs No. of 250 120 100 70 50 students
• b) Using the method of least squares, fit the curves ax? + 2 to the following data. es ee Ee Ee ee [| _» [as [oss [ses [765

• a) Use Romberg’s method, to compute poe dx correct up to two decimal places.
• b) Estimate approximate derivative of f(x) = x? at x=1 for h=0.1, 0.2, 0.05, 0.01. Use first order difference method and find the respective error. ——— i eee 1

• a) Apply the factorization method to solve the equation 3x+2y+7z =4; 2x+3y+z = 5; 3x+4y+z =7
• b) Using SOR method, solve the following system of 4xty+2z = 4; 3x+5y+z = 7; xty+3z = 3.

• a) Find the largest eigen value and the corresponding eigen vector of the matrix 2 -1 -1 2 —1]using power method 0 -1
• b) Using the R-K I* order method, find an approximate value of y i =1, gi OY: YX, = = corresponding to x=1, given that oe and y = 1. When x=0, and h = 0.02.

• a) Using the R-K method of fourth order, solve for y at x= 1.2, 1.4, from dy _ 2xyt+e* . ae 7 xeaxer Given xo=l, yo =0.
• b) Solve the elliptic equation U,, + Uyy = 0 over a square mesh of side four units satisfying the following boundary conditions; u(0,y) = for O< y<4,u(4,y) =12+y for0 <y < 4;u(x,0) = 3x for0< x <4,u(x,4) =x? forO<x <4

Write short notes on: (Any two) 2x5

• a) Shooting Method
• b) Algorithm of Gauss Jordan method
• c) Algorithm of fixed point iteration method és en 2