<s>
In	O
numerical	B-General_Concept
analysis	I-General_Concept
,	O
the	O
Dormand	B-Algorithm
–	I-Algorithm
Prince	I-Algorithm
(	O
RKDP	O
)	O
method	O
or	O
DOPRI	B-Algorithm
method	I-Algorithm
,	O
is	O
an	O
embedded	O
method	O
for	O
solving	O
ordinary	O
differential	O
equations	O
.	O
</s>
<s>
The	O
method	O
is	O
a	O
member	O
of	O
the	O
Runge	B-Algorithm
–	I-Algorithm
Kutta	I-Algorithm
family	O
of	O
ODE	O
solvers	O
.	O
</s>
<s>
Other	O
similar	O
integration	O
methods	O
are	O
Fehlberg	B-Algorithm
(	O
RKF	O
)	O
and	O
Cash	B-Algorithm
–	I-Algorithm
Karp	I-Algorithm
(	O
RKCK	O
)	O
.	O
</s>
<s>
The	O
Dormand	B-Algorithm
–	I-Algorithm
Prince	I-Algorithm
method	I-Algorithm
has	O
seven	O
stages	O
,	O
but	O
it	O
uses	O
only	O
six	O
function	O
evaluations	O
per	O
step	O
because	O
it	O
has	O
the	O
FSAL	O
(	O
First	O
Same	O
As	O
Last	O
)	O
property	O
:	O
the	O
last	O
stage	O
is	O
evaluated	O
at	O
the	O
same	O
point	O
as	O
the	O
first	O
stage	O
of	O
the	O
next	O
step	O
.	O
</s>
<s>
This	O
is	O
the	O
main	O
difference	O
with	O
the	O
Fehlberg	B-Algorithm
method	I-Algorithm
,	O
which	O
was	O
constructed	O
so	O
that	O
the	O
fourth-order	O
solution	O
has	O
a	O
small	O
error	O
.	O
</s>
<s>
For	O
this	O
reason	O
,	O
the	O
Dormand	B-Algorithm
–	I-Algorithm
Prince	I-Algorithm
method	I-Algorithm
is	O
more	O
suitable	O
when	O
the	O
higher-order	O
solution	O
is	O
used	O
to	O
continue	O
the	O
integration	O
,	O
a	O
practice	O
known	O
as	O
local	O
extrapolation	O
(	O
;	O
)	O
.	O
</s>
<s>
Dormand	B-Algorithm
–	I-Algorithm
Prince	I-Algorithm
is	O
currently	O
the	O
default	O
method	O
in	O
the	O
ode45	O
solver	O
for	O
MATLAB	B-Language
and	O
GNU	B-Language
Octave	I-Language
and	O
is	O
the	O
default	O
choice	O
for	O
the	O
Simulink	B-Application
's	O
model	O
explorer	O
solver	O
.	O
</s>
<s>
It	O
is	O
an	O
option	O
in	O
Python	B-Language
's	O
SciPy	O
ODE	O
integration	O
library	O
and	O
in	O
Julia	B-Application
(	O
programming	O
language	O
)	O
'	O
s	O
ODE	O
solvers	O
library	O
.	O
</s>
<s>
Fortran	B-Application
,	O
</s>
