أساليب رونج - كوتا للحل العددي للمعادلة التفاضلية.
d
y
d
t
=
f
(
t
,
y
)
{\displaystyle {\frac {dy}{dt}}=f(t,y)}
والتي تأخذ شكل:
y
n
+
1
=
y
n
+
h
∑
i
=
1
s
b
i
k
i
{\displaystyle y_{n+1}=y_{n}+h\sum _{i=1}^{s}b_{i}k_{i}}
k
1
=
f
(
t
n
,
y
n
)
{\displaystyle k_{1}=f(t_{n},y_{n})}
k
2
=
f
(
t
n
+
c
2
h
,
y
n
+
h
(
a
21
k
1
)
)
{\displaystyle k_{2}=f(t_{n}+c_{2}h,y_{n}+h(a_{21}k_{1}))}
k
3
=
f
(
t
n
+
c
3
h
,
y
n
+
h
(
a
31
k
1
+
a
32
k
2
)
)
{\displaystyle k_{3}=f(t_{n}+c_{3}h,y_{n}+h(a_{31}k_{1}+a_{32}k_{2}))}
k
i
=
f
(
t
n
+
c
i
h
,
y
n
+
h
∑
j
=
1
i
−
1
a
i
j
k
j
)
{\displaystyle k_{i}=f\left(t_{n}+c_{i}h,y_{n}+h\sum _{j=1}^{i-1}a_{ij}k_{j}\right)}