BSc Data Science SEM IV 2022 2023 March 2023 DS NUMERICAL METHODS Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q4 Attempt any THREE questions from the following. 15 marks
   • 2) Use Euler’s method to solve = 1+ y?, with y( 0) =0. Find y(0.1), y(0.2) , y(0.3)
   • 3) Apply Runge-kutta 4" order method to find approximate value of y at x = 0,2, given
   • 4) Use Euler’s modified method to solve = 2y/x with y (1) = 2. Find y (2) with step
   • 5) Given equation = 2y/x with y(1) =2. Estimate y(2) using Adams-Bashforth Moulton method, with = = 4.50, y(1.75) = 6.13
   • 6) using Milne-Simpson’s predictor-corrector method find y at x=0.8 Given equation
2. Q5 Attempt any THREE questions from the following. 15 marks
   • 1) Find QR decomposition of a matrix A = o 2
   • 2) Using Householder’s tridiagonalization method reduce the following matrix into
   • 3) Find largest eigen value of a matrix and corresponding eigen vector of a matrix using Power method where A = 2
   • 4) Using shooting Method, Solve = 2y + 8x(9 — x) with y(0)=0, y(9) = 0. Find
   • 5) Use Inverse Power method to compute smallest eigen value of A with initial vector
   • 6) Using finite difference method, Solve y" — y =x with boundary condition Note: (i) All questions are compulsory
   • (ii) Figures to the right indicate marks for respective questions
3. Q1 Attempt any THREE questions from the following. ) Use Secant method to estimate the root of the equation x* 4x — 10 = 0 with initia! estimates of x; = 4and x2 = 2 15 marks
   • 2) Using Newton Raphson method, find estimate root of x? — 4x — 9 = 0 by taking initial root as 2
   • 3) Estimate the square root of 5 using the equation x* — 5= 0 by applying Fixed point
   • 4) Using Regular falsi method, find the approximate root of — x — 1 = 0. Carry out
   • 5) Using Bisection method, Find the approximate root of equation x* + x — 2 = 0 Perform at-least 5 iterations
   • 6) Write a short note on Absolute error, Relative error and Percentage error
4. Q2 Attempt any THREE questions from the following. ) Use Gauss Elimination method to show that the following system has unique solution 15 marks
   • 2) Define linear system of equations and explain algorithm to solve linear system of
   • 3) Use Gauss seidel method to find the solution of
   • 4) Find LU Decomposition for the matrix A = 0
   • 5) Use Gauss Jordan method to solve,
   • 6) Use LU decomposition method to solve the system of equations,
5. Q3 Attempt any THREE questions from the following. 15 marks
   • 1) Use following table and find and at x = 1.1 by using Newton’s forward
   • 2) U se Newton’s Backward formula to find .5) from the following table

Read from the scan above, so a character or two may differ. The scan is the original.