如何用四阶龙格库塔法求解微分方程

ak47kill

请高手指导大致思路！

jimin

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) 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

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'];

ak47kill

请问%Input - f is the function entered as a string 'f',f为何
望请指教

ak47kill

dy/dx=-y+1  ,y(0)=0;x的范围0到0.5；请问用四阶龙格库塔计算，其中的f是什么啊？

ak47kill

请教高手，dy/dx=-y+1  ,y(0)=0;x的范围0到0.5；这个方程的M文件

AaronSpark

原帖由 ak47kill 于 2006-9-27 18:26 发表
请问%Input - f is the function entered as a string 'f',f为何
望请指教

你要求解的函数

AaronSpark

原帖由 ak47kill 于 2006-9-27 19:51 发表
请教高手，dy/dx=-y+1  ,y(0)=0;x的范围0到0.5；这个方程的M文件

1. function yy=f(t,y);
   
2. yy=-y+1;

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1. R=rk4(@f,0,0.5,0,100)；

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