COMPUTER SCIENCE 2MCA-6 : Computational ... - Surana college

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pc - 708 -2- llillilllffllillllillllllllilllll Answer any two full questions : PART _ B (2x15=30) 2. a) Use Newton Raphson method to find ffi conect to 3 decimal places. 5 b) Find the real root of the equation cos x : 3x - I correct to 3 decimal places using Regula-falsi method lying between 0 and 1. 5 c) Using Bisection method find the root of the equation x log,o x -1.2 that lies between 2 and3 car-ry out 5 iterations. 5 3. a) Using Graeffs root squaring method solve the equation x3 -3*- 6x + 8 : 0. 10 b) Find a root of (x) : e" - 3xzby fixed point iteration method. Choose the initial approximation as zero. 5 4. a) Solve the following system of equations by LU decomposition method 2xr* xz* 4Xr: 12, 4xr* 11x, - x, : 33, 8", - 3xr+ 2xr:20. 8 b) Solve the following equations by relaxation method. 5x-y -z- 3, -X+ 10y -22:7,-x-y+ 102:8. 7 PART - C Answer any two fulI questions : 5. a) Find the dominant eigen value and the corresponding eigen vector of the matrix Io-2 zf n=l-z 3 -rl ^:l- J ' : I using Rayleigh powermethod carry out 5 iterations. 7 L z- -l 3l b) UsingNewton's Divided Difference formula find f(2) given x: 0 | 4 8 10 f(x): -5 -r4 -r25 -21 355 8
lllllllllllllllllllllllllllllllllll -3- pc _ 708 6. a) Forthefollowingdatafind f'(t) and f"(3) g x: 0 2 4 6 8 f(x): 7 13 43 r4S 367 0.3 I "* b) Evaluate Itt-8*')'dx bySimpson's ] Rulebytakingfourordinates. 7 o8 7 . a) using Runge-Kutta method of fourth order, find y(0.2) given # = 3x + j with y (0):1 by taking h:0.1 g b) Using Picard's method find y(0.1) and y (0.2) given * = 1+ xy with y (0) :2.
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COMPUTER SCIENCE 2MCA-6 : Computational ... - Surana college

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