Linear multistep methods are used for the numerical solution of ordinary differential equations. Conceptually, a numerical method starts from an initial...

Euler method. This line of thought can be continued to arrive at various linear multistep methods. The local truncation error of the Euler method is the...

contrasted with implicit linear multistep methods (the other big family of methods for ODEs): an implicit s-step linear multistep method needs to solve a system...

rule is an implicit second-order method, which can be considered as both a Runge–Kutta method and a linear multistep method. Suppose that we want to solve...

In other words, if a linear multistep method is zero-stable and consistent, then it converges. And if a linear multistep method is zero-stable and has...

fourth-order linear multistep method. The method is implicit, but can be made explicit if the differential equation is linear. Numerov's method was developed...

include multistage Runge–Kutta methods that use intermediate collocation points, as well as linear multistep methods that save a finite time history...

it restricts the usefulness of linear multistep methods for stiff equations. An example of a second-order A-stable method is the trapezoidal rule mentioned...

&1\\\end{array}}} The method can also be seen as a linear multistep method with one step. It is the first method of the family of Adams–Moulton methods, and also...

quadrature) numerical methods. Explicit examples from the linear multistep family include the Adams–Bashforth methods, and any Runge–Kutta method with a lower...