Vectors must be the same length

Help me please, I dont know how to solve this problem, line 47 shows 'Vectors must be the same length' , I dont know how to fix it, Thanks for taking time to see my message, Quite urgent.

[KALYAN ACHARJYA]

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[Jin Hao Yen]

% This program implements an explicit scheme to solve the Burgers−Huxley
% eqution, with the addition of shifting the profile. The code ... outputs the
% travelling wave profile, with its corresponding speeds with respect to
% variation in time.
clear all; clc;
% Spacial increment.
dx = 0.1;
% Time increment. 
dt = (0.95)*(1/2)*dx^2;
% Initial spacial domain.
x = [-20:dx:20];
% Time frame for simulation.
T = 600;
% Initial conditions.
u = (1-tanh(x))/2;
% Parameters k,m and n.
pk = 1; pm = 1; pn = 1;

% Defining initail states of paramters that will be used in the program.
iter = 1;
cumshift = 0;
xoffset = 0;
xpos = 0;
tm = 0;
% Implementing a shift every 300th iteration.
for j = 0:dt:T
% Applying a numerical shift every .
if (mod(iter,300)==0)
figure(1)
% Returns indices of the vector "u" that agree with the condition.
ind = find(u>0.1 & u<0.9);
% Returns the x value that corresponds to the u value at 0.5.
xc = interp1(u(ind),x(ind),0.5);
% Determining the number of steps xc is away from 0.
N = floor(xc/dx);
% Creating shift variable.
xshift = N*dx;
% Cumulated shift.
cumshift = cumshift + xshift;
% Rounding error.
xoffset = xc - xshift;
% Creating shifted u.
u = [u(N+1:end) 1,N];
% Shifting x domain.
newx = x+cumshift;
% Plotting shifting wave solution.
plot(newx,u,'b');
axis([newx(1) newx(end) -0.1 1.1])
pause(0.01)
% Adding the total shift to a vector.
xpos = [xpos cumshift+xoffset];
% Adding the accumulated time frames between shits.
tm = [tm j];
end
% Explicit scheme.
u(2:end-1) = u(2:end-1) + ... (dt/(dx)ˆ2).*(u(3:end)−2.*u(2:end−1)+u(1:end−2)) ...
- (dt/(2*dx)).*u(2:end-1).^pk.*(u(3:end) - u(1:end-2)) ... 
+ dt.*u(2:end-1).^pm.*(1-u(2:end-1).^pn);
% Boundary conditions.
u(1) = 1;
u(length(x)) = 0;
iter = iter+1;
end
% Defining parameter values.
sum = 0;
k = 0;
speed(1) = 0;
% Computing the speeds with respect to time.
for j = 2:length(xpos)
    g = (xpos(j)-xpos(j-1))/(tm(j)-tm(j-1));
    sum = sum + g;
k = k+1;
speed(j) = sum/k;
end
figure (4)
% Plotting a Speed vs Time graph.
plot(tm,speed)
fprintf('final speed = %1.9f\n', speed(end));

[Jin Hao Yen]

I am sorry, I am new to this Matlab

[Walter Roberson]

% Creating shifted u.
u = [u(N+1:end) 1,N];

That code does not produce a shifted u. It discards most of u and appends 1 and N to the end of that.

[u(N+1:end) u(1:N)]

would be a rotated u that some might call shifted

Answer 1

[KALYAN ACHARJYA]

% This program implements an explicit scheme to solve the Burgers−Huxley
% eqution, with the addition of shifting the profile. The code ... outputs the
% travelling wave profile, with its corresponding speeds with respect to
% variation in time.
clear all; clc;
% Spacial increment.
dx = 0.1;
% Time increment. 
dt = (0.95)*(1/2)*dx^2;
% Initial spacial domain.
x = [-20:dx:20];
% Time frame for simulation.
T = 600;
% Initial conditions.
u = (1-tanh(x))/2;
% Parameters k,m and n.
pk = 1; pm = 1; pn = 1;
% Defining initail states of paramters that will be used in the program.
iter = 1;
cumshift = 0;
xoffset = 0;
xpos = 0;
tm = 0;
% Implementing a shift every 300th iteration.
for j = 0:dt:T
% Applying a numerical shift every .
if (mod(iter,300)==0)
figure(1)
% Returns indices of the vector "u" that agree with the condition.
ind = find(u>0.1 & u<0.9);
% Returns the x value that corresponds to the u value at 0.5.
xc = interp1(u(ind),x(ind),0.5);
% Determining the number of steps xc is away from 0.
N = floor(xc/dx);
% Creating shift variable.
xshift = N*dx;
% Cumulated shift.
cumshift = cumshift + xshift;
% Rounding error.
xoffset = xc - xshift;
% Creating shifted u.
%u = [u(N+1:end) 1,N];
% Shifting x domain.
newx = x+cumshift;
% Plotting shifting wave solution.
plot(newx,u,'b');
axis([newx(1) newx(end) -0.1 1.1])
pause(0.01)
% Adding the total shift to a vector.
xpos = [xpos cumshift+xoffset];
% Adding the accumulated time frames between shits.
tm = [tm j];
end
% Explicit scheme.
u(2:end-1) = u(2:end-1) + ... (dt/(dx)ˆ2).*(u(3:end)−2.*u(2:end−1)+u(1:end−2)) ...
- (dt/(2*dx)).*u(2:end-1).^pk.*(u(3:end) - u(1:end-2)) ... 
+ dt.*u(2:end-1).^pm.*(1-u(2:end-1).^pn);
% Boundary conditions.
u(1) = 1;
u(length(x)) = 0;
iter = iter+1;
end
% Defining parameter values.
sum = 0;
k = 0;
speed(1) = 0;
% Computing the speeds with respect to time.
for j = 2:length(xpos)
    g = (xpos(j)-xpos(j-1))/(tm(j)-tm(j-1));
    sum = sum + g;
k = k+1;
speed(j) = sum/k;
end
figure (4)
% Plotting a Speed vs Time graph.
plot(tm,speed)
fprintf('final speed = %1.9f\n', speed(end));