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Lorenz (1963) has investigated a system of three first-order differential equations, whose solutions tend toward a " strange attractor ". We show that the same properties can be observed in a simple mapping of the plane defined by: .yi+,= yi+ l-a-K;, yi+l = bx,. Numerical experiments are carried out for a= 1.4, b = 0.3, Depending on the initial point (x,,… (More)

We describe a mechanical device which can be used as an analog computer to solve the transportation problem. In practice this device is simulated by a numerical algorithm. Tests show that this algorithm is 60 times faster than a current subroutine (NAG library) for an average 1000 × 1000 problem. Its performance is even better for degenerate problems in… (More)

Numerical integrations in celestial mechanics often involve the repeated computation of a rotation with a constant angle. A direct evaluation of these rotations yields a linear drift of the distance to the origin. This is due to roundoff in the representation of the sine s and cosine c of the angle θ. In a computer, one generally gets c 2 + s 2 = 1,… (More)

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