`ABM3`

Propagates the state vector forward one time step using the Adams-Bashforth-Moulton 3rd-order method.

Syntax
Description
Input/Output Parameters
See also

Syntax

F = ABM3(f,t,F,h)

Description

F = ABM3(f,t,y,h) updates the $\mathbf{F}$ matrix, F, for the next sample time, given the $\mathbf{F}$ matrix at the current time t, the function f(t,y) defining the ODE $d\mathbf{y}/dt=\mathbf{f}(t,\mathbf{y})$ , and the step size h.

Input/Output Parameters

Variable Symbol Description Format

Input f $\mathbf{f}(t,\mathbf{y})$ multivariate, vector-valued function ( $\mathbf{f}:\mathbb{R}\times\mathbb{R}^{p}\rightarrow\mathbb{R}^{p}$ ) defining the ordinary differential equation $d\mathbf{y}/dt=\mathbf{f}(t,\mathbf{y})$
- 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 1×1
function_handle

t $t_{n}$ current sample time 1×1
double

F $\mathbf{F}$ $\mathbf{F}$ matrix (see Section 3.5.2 of the technical documentation) for the current sample time p×4
double

h $h$ step size 1×1
double

Output F $\mathbf{F}$ $\mathbf{F}$ matrix (see Section 3.5.2 of the technical documentation) for the next sample time p×4
double

	Variable	Symbol	Description	Format
Input	`f`	$\mathbf{f}(t,\mathbf{y})$	multivariate, vector-valued function ( $\mathbf{f}:\mathbb{R}\times\mathbb{R}^{p}\rightarrow\mathbb{R}^{p}$ ) defining the ordinary differential equation $d\mathbf{y}/dt=\mathbf{f}(t,\mathbf{y})$ - 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	1×1 function_handle
	`t`	$t_{n}$	current sample time	1×1 double
	`F`	$\mathbf{F}$	$\mathbf{F}$ matrix (see Section 3.5.2 of the technical documentation) for the current sample time	p×4 double
	`h`	$h$	step size	1×1 double
Output	`F`	$\mathbf{F}$	$\mathbf{F}$ matrix (see Section 3.5.2 of the technical documentation) for the next sample time	p×4 double

ABM3

Contents

Syntax

Description

Input/Output Parameters

See also

`ABM3`