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Linear Multi-step Method

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https://en.wikipedia.org/wiki/Linear_multistep_method

Linear multistep methods are used for the numerical solution of
ordinary differential equations. Conceptually, a numerical method
starts from an initial point and then takes a short step forward in
time to find the next solution point. The process continues with
subsequent steps to map out the solution. Single-step methods (such as
Euler’s method) refer to only one previous point and its derivative to
determine the current value. Methods such as Runge–Kutta take some
intermediate steps (for example, a half-step) to obtain a higher order
method, but then discard all previous information before taking a
second step. Multistep methods attempt to gain efficiency by keeping
and using the information from previous steps rather than discarding
it. Consequently, multistep methods refer to several previous points
and derivative values. In the case of linear multistep methods, a
linear combination of the previous points and derivative values is
used.

线性多步法用于常微分方程的数值解。 从概念上讲,一种数值方法是从一个初始点开始的,然后在时间上向前迈进了一步,以找到下一个求解点。 该过程继续进行后续步骤以制定解决方案。 单步方法(例如欧拉方法)仅引用一个先前的点及其派生变量来确定当前值。 诸如Runge–Kutta之类的方法采取一些中间步骤(例如,半个步骤)以获得更高阶的方法,但是在执行第二个步骤之前,先丢弃所有先前的信息。 多步方法试图通过保留并使用先前步骤中的信息而不是丢弃信息来提高效率。 因此,多步法涉及几个先前的点和导数。 在线性多步法的情况下,使用先前点和导数值的线性组合。

Adams方法基于在区间(tn,tn + 1)内用多项式逼近被积数的想法。 使用k阶多项式可得出k + 1阶方法。 Adams方法有两种类型,显式类型和隐式类型。 显式类型称为Adams-Bashforth(AB)方法,隐式类型称为Adams-Moulton(AM)方法。
一阶AB和AM方法分别只是向前和向后的Euler方法。 这些方法的二阶版本(通过使用线性插值获得)非常流行。 二阶Adams-Bashforth(AB2)方法由

标签:Multi,methods,Adams,multistep,Linear,step,方法,previous
来源: https://blog.csdn.net/qq_18451479/article/details/113824313