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dy
dy = 100(sin t − y), y(0) = 0
y(t) = sin t − 0.01cos t + 0.01e−100t
1.0001
y(3) h = 0.015, 0.020, 0.025, 0.030
R L
V
i(t)R + Ldi(t)
dt − V (t) = 0
di(t)dt
di(t)
dt =
V (t)
L −
i(t)R
L
V (t)
V (t) = V 0 sin t V 0
di(t)
dt
= V 0
L
sin t − i(t)R
L
R
L
V 0
V 0L
= RL
= 100
y = f (t, y(t)) = 100(sin t − y(t))y(t0) = 0
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y(3) 0.15100483254261
y(3)
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y(3)
h
y(t + h) = y(t) + hf (t, y) + y(c)h2
2 , c ∈ int{t, t + h}
y(t) yk y(t + h) = yk+1
yk+1 = yk + hf (tk, yk)tk+1 = tk + hy0 = y(t0)
k = 0, 1, 2, . . . , M − 1
M h
O(h)
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h = 0.020134
M = 149
pk+1 = pk + hf (tk, yk)yk+1 = yk +
h2 (f (tk, yk) + f (tk+1, pk+1)
tk+1 = tk + hy0 = y(t0)
k = 0, 1, 2, . . . , M − 1
O(h2)
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f k,1 = f (tk, yk)
f k,2 = f (tk + h
2 , yk + h
2f k,1)f k,3 = f (tk +
h2 , yk +
h2f k,2)
f k,4 = f (tk + h, yk + hf k,3)
yk+1 = yk + h6 (f k,1 + 2(f k,2 + f k,3) + f k,4)
tk+1 = tk + hy0 = y(t0)
k = 0, 1, 2, . . . , M − 1
h = 0.0345 M = 87
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h
= 0.015
[0, 3]
h = 0.020
h = 0.020134
h = 0.025 h = 0.030
h = 0.034483 h > 0.034884
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h = 0.015
h = 0.020
h = 0.025
h = 0.030
O(h)
O(h2)
O(h4)
h = 0.015
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Orden
y(t)
