AB_coefficients

Coefficients for the mth-order Adams-Bashforth predictor.

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Contents

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 $\mathbf{b}=(b_{1},...,b_{m})^{T}$ storing the coefficients of the mth-order Adams-Bashforth predictor.

AB_coefficients(m,'print') prints the coefficients $b_{1},...,b_{m}$ of the mth-order Adams-Bashforth predictor to the Command Window.

Input/Output Parameters

Variable Symbol Description Format
Input m order of Adams-Bashforth predictor 1×1
double
print - (OPTIONAL) specify as 'print' if you want to print the coefficients to the command window char
Output num - vector storing the numerators of , where stores the coefficients of the mth-order Adams-Bashforth predictor n×1
double
gcd - greatest common denimonator of 1×1
double

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

$$\mathbf{y}_{n+1}=\mathbf{y}_{n}+h\sum_{i=1}^{m}b_{i}\mathbf{f}(t_{n-i+1},\mathbf{y}_{n-i+1})$$

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

See also

AM_coefficients | AB_predictor | AM_corrector | ABM_equations


Published with MATLAB® R2022a