Lax-Wendroff method for advection equation with periodic boundary condition

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Moslem Uddin
Moslem Uddin 2022-3-13
评论： Torsten 2022-3-14
I'm trying to solve advection equation in with and periodic boundary conditions . My approach is as follow:
clc,clear
xmin=0;
xmax=1;
m=400;%space
t=0;
h=1/(m+1);
n=10/(0.95*h);%time steps
a=1;
dt=0.95*h/a;
x=xmin:h:xmax;
a1=a*dt/(h);
% ic
u0=cos(2*pi*x)+.2*cos(10*pi*x);
% plot(x,u0,'k*')
% hold on
u=u0;
un=u0;
% v = VideoWriter('newfile2.avi');
% open(v)
for j=1:n%time
%bc
% u(1)=u(m+1);
for i=2:m+1%space
un(i)=u(i)-(a1/2)*(u(i+1)-u(i-1))+0.5*(a1)^2*(u(i+1)-2*u(i)+u(i-1));
end
un(1)=un(m+1);
un(m+2)=un(2);
u=un;
t=t+dt;
%exact
y_e=(cos(2*pi*(x-t))+.2*cos(10*pi*(x-t)));
plot(x,y_e)
hold on
plot(x,u,'bo-','MarkerFaceColor','r')
hold off
title(sprintf('time=%1.3f',t))
shg
pause(dt)
% frame = getframe(gcf);
% writeVideo(v,frame);
end
% close(v)
error=abs(max(y_e-un))
The code is running well. However, I'm not getting desired order of accuracy. Your help will be appreciated.

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回答（1 个）

Alan Stevens
Alan Stevens 2022-3-13
If you make dt=0.1*h/a; instead of dt=0.95*h/a; your max error reduces to 0.0355.

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