# ABM2

Propagates the state vector forward one time step using the Adams-Bashforth-Moulton 2nd-order method.

## Syntax

F = ABM2(f,t,F,h)


## Description

F = ABM2(f,t,y,h) updates the matrix, F, for the next sample time, given the matrix at the current time t, the function f(t,y) defining the ODE , and the step size h.

## Input/Output Parameters

 Variable Symbol Description Format Input f $\inline&space;\mathbf{f}(t,\mathbf{y})$ multivariate, vector-valued function ($\inline&space;\mathbf{f}:\mathbb{R}\times\mathbb{R}^{p}\rightarrow\mathbb{R}^{p}$) defining the ordinary differential equation $\inline&space;d\mathbf{y}/dt=\mathbf{f}(t,\mathbf{y})$ - inputs to f are the current time (t, 1×1 double) and the current state vector (y, p×1 double) - output of f is the state vector derivative (dydt, p×1 double) at the current time/state 1×1function_handle t $\inline&space;t_{n}$ current sample time 1×1double F $\inline&space;\mathbf{F}$ $\inline&space;\mathbf{F}$ matrix (see Section 3.5.2 of the technical documentation) for the current sample time p×3double h $\inline&space;h$ step size 1×1double Output F $\inline&space;\mathbf{F}$ $\inline&space;\mathbf{F}$ matrix (see Section 3.5.2 of the technical documentation) for the next sample time p×3double