# AM_coefficients

Coefficients for the mth-order Adams-Moulton corrector.

## Syntax

[num,gcd] = AM_coefficients(m)
AM_coefficients(m,'print')

## Description

[num,gcd] = AM_coefficients(m) returns a vector of numerators, num, and the greatest common denominator, gcd, of the vector storing the coefficients of the mth-order Adams-Moulton corrector.

AM_coefficients(m,'print') prints the coefficients of the mth-order Adams-Moulton corrector to the Command Window.

## Input/Output Parameters

 Variable Symbol Description Format Input m $\inline&space;m$ order of Adams-Moulton corrector 1×1double print - (OPTIONAL) specify as 'print' if you want to print the coefficients to the command window char Output num - vector storing the numerators of $\mathbf{b}=(b_{1},...,b_{m})^{T}$, where $\inline&space;\mathbf{b}$ stores the coefficients of the mth-order Adams-Moulton corrector n×1double gcd - greatest common denimonator of $\inline&space;\mathbf{b}$ 1×1double

NOTE: This function assumes the Adams-Moulton corrector is written as

## Example #1

Return the numerators and denominators of the coefficients of the 3rd-order Adams-Moulton corrector.

AM_coefficients returns two quantities; num stores the numerators of the coefficients, while gcd stores the greatest common divisor of the coefficients. The numerators in num are already scaled to be used with gcd.

[num,gcd] = AM_coefficients(3)
num =

5
8
-1

gcd =

12

## Example #2

Print the coefficients of the 3rd-order Adams-Moulton corrector.

AM_coefficients(3,'print');
3th-order Adams-Moulton corrector coefficients:
b(1) = 5/12
b(2) = 8/12
b(3) = -1/12