Jawaharlal Nehru Technological University Hyderabad 2007 M.Tech Computer Aided Structural Engineering NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATION - Question Paper
Sunday, 30 June 2013 10:30Web
ans any 5 ques.
All ques. carry equal marks
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1. Let 1 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 1 dimensional heat formula.
3. discuss Van Neumann stability analysis of matrix methods in the solution to PDEs.
4. provided 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. find the bounds for fault in the solution of a 2 dimensional diffusion formula using Lax Wendroff approach.
6. explain the – convergence of iteration methods to solve large linear systems.
7. Using Galerkain technique to solve Poisson’s formula
uxx + uyy = k2, 0
8.a) discuss different steps involved in finite difference approach.
b) Write weighted residual method with an example.
| Earning: Approval pending. |
