.png){kind=icon}
Return
Generalized Multistep Predictor-Corrector Methods
.png){kind=icon}
OA
AI
DOI：10.1145/321217.321223.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
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.
Journal
No journal information available
Organization
No organization information available
Cited Papers
No cited papers available