Lecture 4 - Computer Science Department - University of Kentucky

General Extrapolation
Extrapolation processes can be applied in more general cases where the error
term can be represented as
E
=
a
h
α
+ b h
β
+ c h
γ
+ L
with 0 < α < β < γ, we show how the first term of the error expansion is
annihilated. Let
α β γ
L = φ( h)
+ a h + b h + c h + L (1)
Replacing h by h/2 yields
h
h α
h β
h γ
L = φ ( ) +
a
( ) +
b
( ) +
c
( ) + L
(2
)
2 2 2 2
Multiplying (2) by 2 α
α
α
h α α h β α h γ
( ) + a h + 2 b ( ) + 2 c ( ) + (3)
2 L = 2 φ
2
2
2
L
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