Code covered by the BSD License

# Numerical Methods Using MATLAB, 3e

### John Mathews (view profile)

20 Aug 2002 (Updated )

Companion Software

M=milne(f,T,Y)
```function M=milne(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 - M=[T' Y'] where T is the vector of abscissas and
%         Y is the vector of ordinates

% NUMERICAL METHODS: MATLAB Programs
%(c) 1999 by John H. Mathews and Kurtis D. Fink
%To accompany the textbook:
%NUMERICAL METHODS Using MATLAB,
%by John H. Mathews and Kurtis D. Fink
%ISBN 0-13-270042-5, (c) 1999
%PRENTICE HALL, INC.

n=length(T);
if n<5, break, end;

F=zeros(1,4);
F=feval(f,T(1:4),Y(1:4));
h=T(2)-T(1);
pold=0;
yold=0;

for k=4:n-1
%Predictor
pnew=Y(k-3)+(4*h/3)*(F(2:4)*[2 -1 2]');
%Modifier
pmod=pnew+28*(yold-pold)/29;
T(k+1)=T(1)+h*k;
F=[F(2) F(3) F(4) feval(f,T(k+1),pmod)];
%Corrector
Y(k+1)=Y(k-1)+(h/3)*(F(2:4)*[1 4 1]');
pold=pnew;
yold=Y(k+1);
F(4)=feval(f,T(k+1),Y(k+1));
end

M=[T' Y'];

```