rk4.m

国外计算机科学教材系列 numerial method using matlab (third edition)

function R=rk4(f,a,b,ya,M)

%Input    - f is the function entered as a string 'f'
%         - a and b are the left and right endpoints
%         - ya is the initial condition y(a)
%         - M is the number of steps
%Output  - R = [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.
%Upper Saddle River, NJ 07458

h=(b-a)/M;
T=zeros(1,M+1);
Y=zeros(1,M+1);
T=a:h:b;
Y(1)=ya;
for j=1:M
   k1=h*feval(f,T(j),Y(j));
   k2=h*feval(f,T(j)+h/2,Y(j)+k1/2);
   k3=h*feval(f,T(j)+h/2,Y(j)+k2/2);
   k4=h*feval(f,T(j)+h,Y(j)+k3);
   Y(j+1)=Y(j)+(k1+2*k2+2*k3+k4)/6;
end

R=[T' Y'];
% a=0,b=3,ya=1,M=50,T4=rk4('f',a,b,ya,M),plot(T4(:,1),T4(:,2))