AM_coefficients

Coefficients for the mth-order Adams-Moulton corrector.

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Contents

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

AM_coefficients(m,'print') prints the coefficients $b_{1},...,b_{m}$ of the mth-order Adams-Moulton corrector to the Command Window.

Input/Output Parameters

Variable Symbol Description Format
Input m order of Adams-Moulton corrector 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-Moulton corrector n×1
double
gcd - greatest common denimonator of 1×1
double

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

$$\mathbf{y}_{n+1}=\mathbf{y}_{n}+h\sum_{i=1}^{m}b_{i}\mathbf{f}(t_{n-i+2},\mathbf{y}_{n-i+2})$$

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

See also

AB_coefficients | AB_predictor | AM_corrector | ABM_equations


Published with MATLAB® R2022a