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Posted By: kondapalli Member Level: Gold Posted Date: 01 May 2008
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2007 Jawaharlal Nehru Technological University M.Tech Process Control APPLIED NUMERICAL METHODS Question paper
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1. Solve the following equations by Gauss-Jordon elimination method.
x1 – x2 + 2x3 = -8
x1 + x2 + x3 = -2
2 x1-2x2 + 3x3 = -20
2. Explain Newton-Raphson method and use it to find the root of x3 – 0.39x2 – 10.5x + 11 = 0 which lies in between 2 and 3.
3. Find the eigen values and eigen vectors of the matrix
??????????121223132
4. Using Newton’s backward difference formula fit a third degree polynomial for the following data:
xi : 1 2 3 4
yi : 7 17 53 157
5. Using Lagrangian interpolation formula fit a polynomial for the data.
xi : 1 3 4 6
yi : 7 53 157 857
6. Apply Runga-kutta fourth order method to find the numerical solution at x = 0.8 for 41.0)4.0(,=+=yyxdxdy assuming the step length h = 0.2
7. Heat and mass transfer in a porous catalyst slab is described by ??????-+-=)1(1)1(exp222yyydxydß?ßf
x=0, dxdy=0 x=1, y=1
Cast these equations into a form suitable for shooting methods. Integrate to obtain y(x) for ? = 20, ß=0.1, f=1.
8. Explain Galerkin Finite Element technique to find the solution of partial differential equations.
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