Index in position 1 is invalid. Array indices must be positive integers or logical values. Error in explicitftcs (line 28) u(Nx+1,k) = 1.; >> u(Nx+1,k) = 1.; Index in

% Heat diffusion in one dimensional wire within the explicit FTCS method

clear;

% Parameters to define the heat equation and the range in space and time

D = 1*10^-4; % Heat Conductivity parameter in m2/s

K = 1*10^-4; % Heat Conductivity parameter in s^-1

L = 5.; % Total length in m

T = 43200.; % Final Time

% Parameters needed to solve the equation within the explicit method

Nt = 7200; % Number of time steps

Dt = T/Nt; % Time step

Nx = 0.1; % Number of space steps in m

Dx = L/Nx; % Space step

b = 1-(2*D*Dt/Dx^2)- K*Dt; % beta parameter in the finite- difference implementation

% Remember that the FTCS method is stable for b=<1

disp(b);

% The initial condition: the initial temperature of the pipe

for i = 1:Nx+1

x(i) = (i-1)*Dx; % we also define vector x, due to the space discretization

u(i,1) = sin (pi*x(i));

end

% Boundary conditions: the temperature of the pipe at the boundaries at any time

for k =1:Nt+1

u(1,k) = 1.;

u(Nx+1,k) = 1.;

t(k) = (k-1)*Dt; % we also define vector t, due to the time discretization

end

% Implementation of the explicit FTCS method

for k =1:Nt % Time Loop

for i=2:Nx; % Space Loop

u(i,k+1) =u(i,k) + 0.5*b*(u(i-1,k)-2.*u(i,k)); % Implementation of the FTCS Method

end

end

%Graphical representation of the temperature at different selected times

Figure(1)

plot(x,u(:,1),'-b',x,u(:,round(Nt/100)),'--g',x,u(:,round(Nt/10)),':b',x,u(:,Nt),'-.r')

Title('Temperature of the pipe within the explicit FTCS method')

xlabel('X')

ylabel('T')

figure(2)

mesh(t,x,u)

title('temperature of the pipe within the explicit FTCS method')

xlabel('t')

ylabel('x')

I need to plot the profile C vs x at t=[2,4,6,8,10,12] hours

[KALYAN ACHARJYA]

More please refer the link below (Only positive integer array Indices are allowed in MATLAB)

link

Answer 1

[Torsten]

Nx should be the number of grid points in x-direction, not the length of these intervals.

You mixed this up by setting Nx = 0.1 instead of 51.

Further, Dx should be L/(Nx-1), not L/Nx.

This update for u is wrong:

u(i,k+1) =u(i,k) + 0.5*b*(u(i-1,k)-2.*u(i,k)); % Implementation of the FTCS Method

Look up the FTCS method again:

https://en.wikipedia.org/wiki/FTCS_scheme

[Naveen Krish]

Which is the right update for u can you say whats that? I couldn't able to get it from the link

[Torsten]

The 1d heat equation is explicitly discretized in the paragraph

Illustration: one-dimensional heat equation

I think the update is very clearly written there.

[Naveen Krish]

u(i,k+1) =u(i,k) + ((D*Dt/Dx^2)*Dt/Dx^2)(u(i+1,k)-2.*u(i,k)+u(i-1,k)); % Implementation of the FTCS Method

Is this correct?

[Torsten]

I only see

u(i,k+1) =u(i,k) + D*Dt/Dx^2*(u(i+1,k)-2*u(i,k)+u(i-1,k)); % Implementation of the FTCS Method

Where do you get the extra Dt/Dx^2 from ?

[Naveen Krish]

Got it but when i run my code my figure 2 is not showing

[Torsten]

Didn't you read in the MATLAB documentation that you must first apply meshgrid on the t and x vectors ?

https://de.mathworks.com/help/matlab/ref/mesh.html

[Naveen Krish]

How should i apply meshgrid? i'm not quite familiar with that. And the documentation i cant able to relate it to my problem

Answer 2

[Image Analyst]

There is a thorough discussion of the error in the FAQ:

https://matlab.fandom.com/wiki/FAQ#.22Subscript_indices_must_either_be_real_positive_integers_or_logicals..22