function [] = Wave1d(N,m,T)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Wave1d solves wave equation using Explicit scheme. N: no of x axis mesh intervals, m: no of time
% intervals, T: final time
% It also compares the solutions for the equation:
% u_tt-u_xx=0, u(x,0)=sin(pi x), u_t(x,0)=0, u(0,t)=0=u(1,t)

% Exact solution: u(x,t)=sin(pi*x)*cos(pi*t)

% Run with typing in command window: a) Wave1d(100,100,1) b) Wave1d(50,500,0.1) c) Wave1d(10,10,0.1)
% d) Wave1d(1000,100,0.1)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

dx=1/N
dt=T/m
xx=0:dx:1;
tt=0:dt:T;

uu=@(x,t) sin(pi*x).*cos(pi*t);
[XX,TT]=meshgrid(xx,tt);
U=uu(XX,TT);

l=dt/dx;
CFL=l
e=ones(N-1,1);

A=spdiags([l*l*e 2*(1-l*l)*e l*l*e],[-1 0 1],N-1,N-1);
u=zeros(m+1,N+1);
u(1,:)=sin(pi*xx);
b=u(1,2:N);
u(2,2:N)=(A/2)*b';
for n=2:m
    b=u(n,2:N)';
    temp=A*b-u(n-1,2:N)';
    u(n+1,2:N)=temp';
end

mesh(xx,tt,u)

xlabel('x');
ylabel('t');
title('Solution of Wave equation : Explicit')
Error_Wave =norm(u-U,Inf)