RK2 and modified euler's method

11 次查看（过去 30 天）

Ammar Alsenani 2019-4-4

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/454390-rk2-and-modified-euler-s-method

a=1;
b=2;
w0=1;
h=[0.5 0.1 0.05 0.01 0.005 0.001];
f=@(t,w) (w/t)-(w/t)^2;
wnA=zeros(1,6);
RE_mod=zeros(1,6);
wnB=zeros(1,6);
RE_mid=zeros(1,6);
for i=1:6
    w=w0;
    t=a;
    for j=1:(b-a)/h(i)
        w=w+h(i)*f(t,w);
        t=a+j*h(i);
    end
    wnA(i)=w;
    RE_mod(i)=abs(t/(log(t)+1));
end
for i=1:6
    w=w0;
    t=a;
    tic
    for j=1:(b-a)/h(i)
        w=w+h(i)*f(t+h/2,w+h/2*f(t,w));
        t=a+j*h(i);
        time=toc;
    end
    wnB(i)=w;
    RE_mid(i)=abs(t*log(t)+2*t);
end
loglog(h,RE_mid,'-+',h,RE_mod,'-o')
legend('Midpoint=RK2','Modified Euler')
xlabel('h')
ylabel('Relative Error')
%%this is my code but somthing is wrong with it, the graphs are strirtght horizental lines.