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anonymous
 5 years ago
Suppose that the differential equation dx/dt = f(x) has a stationary point x* where f'(x*) < 0. We saw that the point x* is a stable fixed point for x{n}+1 = x{n} + hf(x{n}), provided that h < 2/f'(x*). Assuming that x{0} is sufficiently close to x*, show that if h > 1/f'(x*) then x{n} is alternately greater than and less than x*, while if h < 1/f'(x*) the orbit x{n} approaches x* monotonically.
WTF. ({...} = subscript)
anonymous
 5 years ago
Suppose that the differential equation dx/dt = f(x) has a stationary point x* where f'(x*) < 0. We saw that the point x* is a stable fixed point for x{n}+1 = x{n} + hf(x{n}), provided that h < 2/f'(x*). Assuming that x{0} is sufficiently close to x*, show that if h > 1/f'(x*) then x{n} is alternately greater than and less than x*, while if h < 1/f'(x*) the orbit x{n} approaches x* monotonically. WTF. ({...} = subscript)

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