clear;
format long;
ns=200;
x=linspace(0,2,ns);
dt=1e-05; dx=x(2)-x(1); dell=0.022^2;

um1=cos(pi*x);
for i=3:ns-2,
u(i)=um1(i)-(1/6)*(dt/dx)*(um1(i+1)+um1(i)+um1(i-1))*(um1(i+1)-um1(i-1))-(dell*dt/(2*dx^3))*(um1(i+2)-2*um1(i+1)+2*um1(i-1)-um1(i-2));
end;
i=2;
u(i)=um1(i)-(1/6)*(dt/dx)*(um1(i+1)+um1(i)+um1(i-1))*(um1(i+1)-um1(i-1))-(dell*dt/(2*dx^3))*(um1(i+2)-2*um1(i+1)+2*um1(i-1)-um1(ns));
i=ns-1;
u(i)=um1(i)-(1/6)*(dt/dx)*(um1(i+1)+um1(i)+um1(i-1))*(um1(i+1)-um1(i-1))-(dell*dt/(2*dx^3))*(um1(1)-2*um1(i+1)+2*um1(i-1)-um1(i-2));
i=1;
u(i)=um1(i)-(1/6)*(dt/dx)*(um1(i+1)+um1(i)+um1(ns))*(um1(i+1)-um1(ns))-(dell*dt/(2*dx^3))*(um1(i+2)-2*um1(i+1)+2*um1(ns)-um1(ns-1));
i=ns;
u(i)=um1(i)-(1/6)*(dt/dx)*(um1(1)+um1(i)+um1(i-1))*(um1(1)-um1(i-1))-(dell*dt/(2*dx^3))*(um1(2)-2*um1(1)+2*um1(i-1)-um1(i-2));

it1=1;
it=1;

while ((it-1)*dt<5)


for i=3:ns-2,
u1(i)=um1(i)-(1/3)*(dt/dx)*(u(i+1)+u(i)+u(i-1))*(u(i+1)-u(i-1))-(dell*dt/(dx^3))*(u(i+2)-2*u(i+1)+2*u(i-1)-u(i-2));
end;
i=2;
u1(i)=um1(i)-(1/3)*(dt/dx)*(u(i+1)+u(i)+u(i-1))*(u(i+1)-u(i-1))-(dell*dt/(dx^3))*(u(i+2)-2*u(i+1)+2*u(i-1)-u(ns));
i=ns-1;
u1(i)=um1(i)-(1/3)*(dt/dx)*(u(i+1)+u(i)+u(i-1))*(u(i+1)-u(i-1))-(dell*dt/(dx^3))*(u(1)-2*u(i+1)+2*u(i-1)-u(i-2));
i=1;
u1(i)=um1(i)-(1/3)*(dt/dx)*(u(i+1)+u(i)+u(ns))*(u(i+1)-u(ns))-(dell*dt/(dx^3))*(u(i+2)-2*u(i+1)+2*u(ns)-u(ns-1));
i=ns;
u1(i)=um1(i)-(1/3)*(dt/dx)*(u(1)+u(i)+u(i-1))*(u(1)-u(i-1))-(dell*dt/(dx^3))*(u(2)-2*u(1)+2*u(i-1)-u(i-2));

if (mod(it,1000)==0)

us(:,it1)=u;

it1=it1+1;
end;

um1=u;
u=u1;
it=it+1;

end;