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Unformatted text preview: Tutorial 3 Question 1 Given a function, g = G, , derive a central difference approximation for the second cross-derivative, , of the highest order possible with the points indicated. Subscript notation for , grid Simpler notation Question 2 Apply Newtons method to find all the finite roots of: 1 + 2 = Explain what happens with the following initial guesses: (a) = 0 , (b) = 0.05 , (c) = 0.1 , (d) = 0.5 , and (e) = 1 . Question 3 The flow rate, , in a system is given by, = 15 7.510 80 + 10.5 u . Set up a direct iteration scheme, including relaxation, to solve this equation in the given form. Using an initial guess of = 5, investigate what happens with, i) = 1 (no relaxation) and ii) = 0.25 (under-relaxation). Question 4 Solve the following nonlinear system of equations by Gauss-Seidel iteration with (a) no relaxation, and (b) an under-relaxation constant of = 0.8 : (1)...
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This note was uploaded on 09/16/2011 for the course ME 303 taught by Professor Serhiyyarusevych during the Spring '10 term at Waterloo.
- Spring '10