Problem with plotting 1D heat diffusion using FTCS

Hello, I have this issue with the plot where there is a sudden spike at the temperature near x and t are 0. I can't seem to find the problem with the code. The initial temperature is T(x,0) = x, and the ends of a 1m wire is insulated.

%FTCS march 9
clc;
clear;

c = 1; %alpha, thermal constant
L = 1; %wire length
T = 0.3; %total time

Nt = 6500; %time steps
Dt = T/Nt;
Nx = 100; %space steps
Dx = L/Nx;
b = c*Dt/(Dx*Dx); %must not exceed 1/2

fprintf ('b = %.2f \n', b);

b = 0.46 

%Initial conditions
for i=1:Nx+1
    x(i) = (i-1)*Dx;
    u(i,1) = x(i);
end

%boundary Conditions
for k=1:Nt+1
    u(1,k)= 0;
    u(end,k)=0;
    t(k)= (k-1)*Dt;
end

%FTCS
for k=1:Nt
    for i=2:Nx
        u(i,k+1) = u(i,k) + b.*(u(i-1,k)+u(i+1,k)-2.*u(i,k));
    end
end


mesh(t,x,u)
title ('Plot of time and space')
xlabel('t')
ylabel('x')
zlabel('u')

[Torsten]

If you start with

u(i,1) = x(i); 

and set

u(1,k)= 0;
u(end,k)=0;

as boundary condition, there will be a discontinuity at x = 1.

Is it that what you mean ?