abm模型MATLAB：Matlab实现Adams-Bashforth方法

abm.m

function A = abm(f,T,Y)

%Input - f is the function entered as a string 'f'

% - T is the vector of abscissas

% - Y is the vector of ordinates

%Remark. The first four coordinates of T and Y must

% have starting values obtained with RK4

%Output - A=[T?? Y??] where T is the vector of abscissas

% and Y is the vector of ordinates

n=length(T);

if n>=5

F=zeros(1,4);

F=feval(f, T(1:4), Y(1:4));

h=T(2)-T(1);

for k=4:n-1

%Predictor

p=Y(k)+(h/24)*(F*[-9 37 -59 55]');

T(k+1)=T(1)+h*k;

F=[F(2) F(3) F(4) feval(f, T(k+1), p)];

%Corrector

Y(k+1)=Y(k)+(h/24)*(F*[1 -5 19 9]');

F(4)=feval(f, T(k+1), Y(k+1));

end

A=[T' Y'];

end

fun1.m

function f=fun1(t,y)

f=t.^2-y;

Untitlel.m

T=[0,0.05,0.10,0.15,0.20,0.25,0.03];

Y=[1,0.95127058,0.90516258,0.86179202,0,0,0];

f='fun1';

A=abm(f,T,Y)

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