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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 Computer Aided Structural Engineering NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATION Question paper
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Answer any FIVE questions
All questions carry equal marks
- - -
1. Let one dimensional PDE be Vt = Vxx with
v=0 at x=0 ?t
v=0 at x=1 ?t
v=2x at t=0 for 0 = x = 0.5
v=2(1-x) at t=0 for 0.5 = x = 1.
Solve crank Nicolson method by taking h=1 and k=0.001.
2. Write an explicit method of finite difference approximation to one dimensional heat equation.
3. Explain Van Neumann stability analysis of matrix methods in the solution to PDEs.
4. Given the elliptic PDE, .022222=++OyvOOxvO The closed boundary is a square bounded by x=±1, y=±1 and
v=0 for y=1, -1 = x = 1
v=1 for y=-1, -1 = x = 1.
The boundary conditions are
vx = -v/2, -1 = y = 1, x=1.
vy = v/2, -1 = y = 1, x=-1.
5. Obtain the bounds for error in the solution of a two dimensional diffusion equation using Lax Wendroff approach.
6. Discuss the – convergence of iteration methods to solve large linear systems.
7. Using Galerkain technique to solve Poisson’s equation
uxx + uyy = k2, 0write u=0 on the boundary C of the region.
8.a) Explain various steps involved in finite difference approach.
b) Write weighted residual method with an example.
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