Midpoint method

In numerical analysis, a branch of applied mathematics, the midpoint method is a one-step method for numerically solving the differential equation,

The explicit midpoint method is given by the formula

the implicit midpoint method by

for $n=0,1,2,\dots$ Here, $h$ is the step size — a small positive number, $t_{n}=t_{0}+nh,$ and $y_{n}$ is the computed approximate value of $y(t_{n}).$ The explicit midpoint method is also known as the modified Euler method, the implicit method is the most simple collocation method, and, applied to Hamiltionian dynamics, a symplectic integrator.

单词	Midpoint method
释义	Midpoint method 英语百科 Midpoint method In numerical analysis, a branch of applied mathematics, the midpoint method is a one-step method for numerically solving the differential equation, The explicit midpoint method is given by the formula the implicit midpoint method by for $n=0,1,2,\dots$ Here, $h$ is the step size — a small positive number, $t_{n}=t_{0}+nh,$ and $y_{n}$ is the computed approximate value of $y(t_{n}).$ The explicit midpoint method is also known as the modified Euler method, the implicit method is the most simple collocation method, and, applied to Hamiltionian dynamics, a symplectic integrator.
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