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Download B.Tech. Semester 3 Computational Methods PYQ year 2023-24 and more Exams Computational Methods in PDF only on Docsity!
t_ 7 (Please write your Exam Roll No.) Exam Rolt END TERM EXAMINATION THIRD SEMESTER [B.TECH] DECEMBER-2024 Paper Code: ES-201 Subject: Computational Methods Time: 3 Hours Maximum Marks: 60 Note: Attempt five questions in all including Q. no.1 which is compulsory. Select one question from each unit. Scientific. calculator ts allowed. al ov (a) Determine the decimal number that correspond to the machine word. YY kof [45DE4000)15, i (2) (b) Using secant method find the root of x sin(x)— 3 cos(x) = 0 between (0.0, 1.8) eA with accuracy of 2 digits after decimal point. (3) ae For following given set of data for x & y, formulate the Newton divided differences table. (3) [x 0.00. |2.00 [4.00 | 6.0 8.0 J ly 0.00 8.00 64.00 | 216.00 | 512.00 (ay Compute i HAO) de by using the composite Trapezoid rule with six uniform points. Assign the value (a =1atx=0. (3) (et Define Decomposition of any matrix. Explain the required condition for — Doolittle and Crout decomposition method. . (2) c- Find the value of A for which the system of equations ey aah, xt2y-22=1 & Axty+z=1, will have unique solution. (3) 48) Using Euler’s method find the value of y at x=0.10 of the ODE t \ ¢ =x+y+xy Where initial conditions are Xo = 0.00 & yp = 1.00 and using s 2 Le ‘step size 0.10. . : (3) i Give an example and conditions of Parabolic, Hyperbolic and Elliptic partial differential equations. (1) UNIT —1 Q2 (a) Find the value of function f(x) = 1—cos(x) atx = 0.1. Modify the expression so. that loss of significant digits can be avoided and calculate the value again. Compare two values with the true value 0.4996 x 107. (5) (b) Define rate of convergence and stability of iterative method. Prove that the rate of convergence of Newton-Raphson method is 2. (5) Q3. a4 Define Multivariate unconstraint minimization problem with an example. Using Newton Method to minimize multivariate function, minimize f(x") = 2 4 x2 — 2x,x, starting at xk = [1,1]", where x® = [xq x2)" . (5) etermine the minimum point of the function f(x) = x2—7x+12 by Fibonacci search method, if the first uncertainty interval is [2,4] . (5) P.T.O. f-\/3 rg-20! 
