Assignment 2
September 17, 2014
1. Assume that the motion of a particle is govern by the equation
ẋ = a11 x + a12 y
and ẏ = a21 x + a22 y.
or
ẋ = Ax.
What are the conditions that makes the flow periodic, decaying or growing? Give an
example (choose A) for each case.
2. The Lorenz equations are
ẋ = σ(y − x)
ẏ = x(ρ − z) − y
ż = xy − βz
We let σ = 10, β = 8/3 and ρ = 28.
(a) Use the forward Euler method to integrate the problem starting from the point
(1, 1, 1). Run it with sufficiently small time steps until you feel that your solution
is valid for t = 3.
(b) Change the initial condition to be (1, 1, 1.01) and report your finding.
(c) Use matlab’s ode45 for the solution of the 2 problems above and compare the
results
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