untitled3.m

利用MATLAB进行求解常微分方程组的四阶R-K算法法

clear;
%程序C8-4  三阶预估-校正法
t(1)=1;y(1)=1;h=1.0;n=1;ff=zeros(1,5);
N=6;%迭代次数
while t<3
    t(n)=n*h;
    ff(n)=f_m(y(n),t(n));
    K1=h*f_m(y(n),t(n));
    K2=h*f_m(y(n)+0.5*K1,t(n)+0.5*h);
    K3=h*f_m(y(n)+0.5*K2,t(n)+0.5*h);
    K4=h*f_m(y(n)+K3,t(n)+h);
    y(n+1)=y(n)+(K1+2*K2+2*K3+K4)/6;
    n=n+1;
end
%y(1)=[];
for i=2:N-1
    y(i+1)=y(i)+(h/12)*(23*f_m(y(3),t(3))-16*f_m(y(2),t(2))+5*f_m(y(1),t(1)));
    t(i+1)=(i+1)*h;
    ff(5)=f_m(y(i+1),t(i+1));
%     y(i+1)=y(i)+(h/12)*(5*ff(5)+8*ff(4)-ff(3));
    y(i+1)=y(i)+(h/12)*(5*ff(5)+8*f_m(y(i),t(i))-f_m(y(i-1),t(i-1)));
    ff(5)=f_m(y(i+1),t(i+1));
    for j=1:4
        ff(j)=ff(j+1);
    end
end
plot(t,y);
y