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Differential Equations Solutions 101

# Differential Equations Solutions 101 - 3 s 2...

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111 0 5 10 15 20 25 30 35 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 day Proportion of individuals Disease Status with tau = 0.200000, delta = 0.010000 Infected Susceptible Recovered Figure 19.2. Proportion of individuals infected by day in a 10 × 10 grid of hospital beds, with infection rate τ = 0 . 2 and mobility rate δ = 0 . 01 . in them at time 1. (c) If A is a dense matrix, then computing A ( Ae 1 ) costs 2 s 2 multiplications, where s is the number of states. Computing ( A 2 ) e 1 costs s 3
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Unformatted text preview: 3 + s 2 multiplications, and this is quite a bit more when s is large. (We should also take advantage of the zeros in A and avoid multiplying by them. If we do this for our matrix, A has 21 nonzero elements while A 2 has 23, so again it takes more multiplications to form ( A 2 ) e 1 than to form A ( Ae 1 ). We should also note that the product Ae 1 is just the Frst...
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