Why is my error not exactly 0

Question

Nicholas Zhao 2024-4-13，22:57

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2106546-why-is-my-error-not-exactly-0

回答： Image Analyst 2024-4-13，23:11

在 MATLAB Online 中打开

I wrote a very simple upwind difference scheme for the equation

with

, but for some reason the error is not exactly 0.

%u_t+u_x=0
space=[0.01,0.005,0.0025,0.00125];
error=zeros(size(space));
for j=1:size(space,2)
    dx=space(j);
    dt=dx;
    u=sin(0:dx:1);
    n=size(u,2);
    T=1/dt;
    for i=1:1
        ul=[sin(-dx-dt*(i-1)),u(1:(n-1))];
        u=(1-dt/dx)*u+ul*dt/dx;
    end
    error(j)=norm(u-sin((0:dx:1)-dt),1)/n;
end