{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

math572_hw4 - MATH 572 Assignment#4 Numerical Methods for...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH 572 Numerical Methods for Scientific Computing II Winter 2005 Assignment #4 due : Thursday , March 10 1. Consider the 2-step BDF scheme, u n + 1 2 2 u n = hf ( u n ). a) Find the characteristic roots ζ 1 ( h ) , ζ 2 ( h ) for the test equation and plot them using Matlab over the interval - 10 0. b) Show analytically that the negative real axis is contained in the region of absolute stability. (Note: the scheme is actually A-stable, but it is not required to show that here.) 2. The Lorenz system is defined by y 1 y 2 y 3 = σ ( y 2 - y 1 ) ry 1 - y 2 - y 1 y 3 y 1 y 2 - by 3 . These equations were originally derived as a model for thermal convection; the variables represent the temperature, density, and velocity in a certain fluid flow. It was discovered by numerical computations that the parameters σ = 10 , b = 8 / 3 , r = 28 yield a system with chaotic dynamics. Solve this system with initial conditions y 1 (0) = 0 , y 2 (0) = 1 , y 3 (0) = 0 up to time t = 100 using Matlab’s ode45 solver. (Part of the exercise is to read the online
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}