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摘要
En 中文
The order
p
which is obtainable with a stable
k
-step method in the numerical solution of
y′
=
f
(
x
,
y
) is limited to
p
=
k
+ 1 by the theorems of Dahlquist. In the present paper the customary schemes are modified by including the value of the derivative at one “nonstep point;” as usual, this value is gained from an explicit predictor. It is shown that the order of these generalized predictor-corrector methods is not subject to the above restrictions; stable
k
-step schemes with
p
= 2
k
+ 2 have been constructed for
k
≤ 4. Furthermore it is proved that methods of order
p
actually converge like
h
p
uniformly in a given interval of integration. Numerical examples give some first evidence of the power of the new methods.
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