# AB_coefficients

Coefficients for the mth-order Adams-Bashforth predictor.

## Syntax

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


## Description

[num,gcd] = AB_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-Bashforth predictor.

AB_coefficients(m,'print') prints the coefficients of the mth-order Adams-Bashforth predictor to the Command Window.

## Input/Output Parameters

 Variable Symbol Description Format Input m $\inline&space;m$ order of Adams-Bashforth predictor 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-Bashforth predictor n×1double gcd - greatest common denimonator of $\inline&space;\mathbf{b}$ 1×1double

NOTE: This function assumes the mth-order Adams-Bashforth predictor is written as

## Example #1

Return the numerators and denominators of the coefficients of the 3rd-order Adams-Bashforth predictor.

AB_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] = AB_coefficients(3)

num =

23
-16
5

gcd =

12



## Example #2

Print the coefficients of the 3rd-order Adams-Bashforth predictor.

AB_coefficients(3,'print');

3th-order Adams-Bashforth predictor coefficients:
b(1) = 23/12
b(2) = -16/12
b(3) = 5/12