Using the Lax Method to solve 1D wave equation

Anonymous123

2020 6 27

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Needing help to see why my code will only plot the exact solution and breaks during the numerical solution, thanks.

% Lax Method
N=40; %No. of grid points
Tmax=1; % time period
alpha=1;  %given
h=1; %given value of delX
% Lax Method
delt=1;
maxt=Tmax/delt; %Number of time steps
c=alpha*delt/h; 
u=zeros(N+1,maxt+1);
x=zeros(N+1,1);
% Initial condition
for i=1:N+1
  x(i)=(i-1)*h;
  u(i,1)=sin((2*pi*x(i)/40));
end
for k=1:maxt
  u0 = u(N,k);
  u(1,k+1)=(1-c)/2*(u(2,k)-u0)+(1+c)/2*(u(2,k));
  for i=2:N
    u(i,k+1) =(1-c)/2*(u(i+1,k)+(1+c))/2*(u(i+1,k));
  end
  uNp2 = u(2,k);
  u(N+1,k+1) =(1-c)/2*(uNp2-u(N,k))+(1+c)/2*(uNp2-2*u(N+1,k));  
end
plot(x,u)