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implicit midpoint method
a one-step numerical method for solving differential equations
midpoint method
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Statements
instance of
midpoint methods
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Gauss–Legendre method
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collocation method
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symplectic integrator
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defining formula
y
n
+
1
=
y
n
+
h
f
(
t
n
+
h
2
,
1
2
(
y
n
+
y
n
+
1
)
)
{\displaystyle y_{n+1}=y_{n}+hf\left(t_{n}+{\frac {h}{2}},{\frac {1}{2}}\left(y_{n}+y_{n+1}\right)\right)}
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has characteristic
order of convergence
of
global error
numeric value
2
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number of stages
quantity
1
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maintained by WikiProject
WikiProject Mathematics
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Butcher tableau
1
/
2
1
/
2
1
{\displaystyle {\begin{array}{c|c}1/2&1/2\\\hline &1\end{array}}}
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opposite of
explicit midpoint method
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Â
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