function A=abm(f,T,Y) %Input - f is the function % - 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 % If f is an M-file function call A=abm(@,f,T,Y). % If f is an anonymous function call A=abm(f,T,Y). % NUMERICAL METHODS: Matlab Programs % (c) 2004 by John H. Mathews and Kurtis D. Fink % Complementary Software to accompany the textbook: % NUMERICAL METHODS: Using Matlab, Fourth Edition % ISBN: 0-13-065248-2 % Prentice-Hall Pub. Inc. % One Lake Street % Upper Saddle River, NJ 07458 n=length(T); if n F=zeros(1,4); F=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) f(T(k+1),p)]; %Corrector Y(k+1)=Y(k)+(h/24)*(F*[1 -5 19 9]'); F(4)=f(T(k+1),Y(k+1)); end A=[T' Y'];
