<s>
In	O
numerical	B-General_Concept
analysis	I-General_Concept
,	O
predictor	B-Algorithm
–	I-Algorithm
corrector	I-Algorithm
methods	I-Algorithm
belong	O
to	O
a	O
class	O
of	O
algorithms	O
designed	O
to	O
integrate	O
ordinary	O
differential	O
equationsto	O
find	O
an	O
unknown	O
function	O
that	O
satisfies	O
a	O
given	O
differential	O
equation	O
.	O
</s>
<s>
When	O
considering	O
the	O
numerical	B-General_Concept
solution	I-General_Concept
of	O
ordinary	O
differential	O
equations	O
(	O
ODEs	O
)	O
,	O
a	O
predictor	B-Algorithm
–	I-Algorithm
corrector	I-Algorithm
method	I-Algorithm
typically	O
uses	O
an	O
explicit	B-Algorithm
method	I-Algorithm
for	O
the	O
predictor	O
step	O
and	O
an	O
implicit	B-Algorithm
method	I-Algorithm
for	O
the	O
corrector	O
step	O
.	O
</s>
<s>
A	O
simple	O
predictor	B-Algorithm
–	I-Algorithm
corrector	I-Algorithm
method	I-Algorithm
(	O
known	O
as	O
Heun	B-Algorithm
's	I-Algorithm
method	I-Algorithm
)	O
can	O
be	O
constructed	O
from	O
the	B-Algorithm
Euler	I-Algorithm
method	I-Algorithm
(	O
an	O
explicit	B-Algorithm
method	I-Algorithm
)	O
and	O
the	O
trapezoidal	B-Algorithm
rule	I-Algorithm
(	O
an	O
implicit	B-Algorithm
method	I-Algorithm
)	O
.	O
</s>
<s>
First	O
,	O
the	O
predictor	O
step	O
:	O
starting	O
from	O
the	O
current	O
value	O
,	O
calculate	O
an	O
initial	O
guess	O
value	O
via	O
the	B-Algorithm
Euler	I-Algorithm
method	I-Algorithm
,	O
</s>
<s>
Next	O
,	O
the	O
corrector	O
step	O
:	O
improve	O
the	O
initial	O
guess	O
using	O
trapezoidal	B-Algorithm
rule	I-Algorithm
,	O
</s>
<s>
There	O
are	O
different	O
variants	O
of	O
a	O
predictor	B-Algorithm
–	I-Algorithm
corrector	I-Algorithm
method	I-Algorithm
,	O
depending	O
on	O
how	O
often	O
the	O
corrector	O
method	O
is	O
applied	O
.	O
</s>
