errores edos
DESCRIPTION
errores EDOsTRANSCRIPT
7/17/2019 Errores edos
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dy
dt = f (t, y(t)), y(t0) = y0
[a, b]
{tk, yk}
y(tk) ≈ yk
[a, b]
M
tk = a + kh, k = 0, 1, · · · , M, h = b − a
M
h
y(t)
t = t0
y(t) = y(t0) + y′(t0)(t − t0) + y′′(t0)(t − t0)2
2 .
y′(t0) = f (t0, y(t0)) h = t1 − t0
y(t1) = y(t0) + hf (t0, y(t0)) + y ′′(t0)h2
2
h2
y(t1) ≈ y1 = y0 + hf (t0, y0)
yk
y = y(t)
k
tk+1 = tk + h, yk+1 = yk + hf (tk, yk), k = 0, 1, · · · , M − 1
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tk+1 = tk + h, yk+1 = yk + hφ(tk, yk), k = 0, 1, · · · , M − 1
φ
{tk, yk}M
k0
y = y(t)
ek
ek = |y(tk) − yk|, k = 0, 1, · · · , M − 1
k
ǫk+1
tk
tk+1
ǫk+1 = |y(tk+1) − (y(tk) + hφ(tk, y(tk))| , k = 0, 1, · · · , M − 1
E (y(b), h) = |y(b) − yM |
h, h
2, h4
, · · ·
h
E (y(b), h) ∝ (hn)
n
O(hn)