finite difference method, why the result is zero?

Question

sing lai 2014-4-17

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/126106-finite-difference-method-why-the-result-is-zero

 function [u,x,t] = wave(a,xf,T,it01,it02,i1t0,bx0,bxf,M,N)
%solve a u_xx = u_tt for 0<=x<=xf, 0<=t<=T
% Initial Condition: u(x,0) = it0(x), u_t(x,0) = i1t0(x)
% Boundary Condition: u(0,t)= bx0(t), u(xf,t) = bxf(t)
% M = # of subintervals along x axis
% N = # of subintervals along t axis
%solve_wave
a = 1; h=0.005; d=0.16; L=0.64
it01 = inline('h*x./d','x');
it02 = inline('h*(L-x)./(L-d)','x');
i1t0 = inline('0'); %initial condition
bx0 = inline('0'); bxf = inline('0'); %boundary condition
xf = 1; M = 20; T = 20; N = 50;
 dx = xf/M; x = [0:M]'*dx;  %space step size
dt = T/N; t = [0:N]*dt;    %time step size
for i = 1:M + 1
    if 'x' >= 0 && 'x' <= d
        u(i,1)=it01(x(i));
    elseif 'x' >= d && 'x' <= L
        u(i,1)=it02(x(i));
    end
end
for k = 1:N + 1
u([1 M + 1],k) = [bx0(t(k)); bxf(t(k))];
end
r = a*(dt/dx)^ 2; r1 = r/2; r2 = 2*(1 - r);
u(2:M,2) = r1*u(1:M - 1,1) + (1 - r)*u(2:M,1) + r1*u(3:M + 1,1) ...
    + dt*i1t0(x(2:M)); 
for k = 3:N + 1
u(2:M,k) = r*u(1:M - 1,k - 1) + r2*u(2:M,k-1) + r*u(3:M + 1,k - 1)...
    - u(2:M,k - 2); 
end
 figure(1), clf
mesh(t,x,u)
ylabel('x', 'FontSize', 16);
xlabel('t', 'FontSize', 16);
zlabel('u', 'FontSize', 16);
figure(2), clf
for n = 1:N %dynamic picture
plot(x,u(:,n)), axis([0 xf -0.3 0.3]), pause(0.2)
xlabel('t', 'FontSize', 16);
ylabel('u', 'FontSize', 16);
end

I using finite difference method to solve the wave equation of pluked string, but why the result come out all zero? anyone can help me solve the problem is much appreciated, thanks!