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

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Naveen Krish
Naveen Krish 2022-4-3
评论： Naveen Krish 2022-4-3
% 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

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回答（2 个）

Torsten
Torsten 2022-4-3
编辑：Torsten 2022-4-3
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
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Naveen Krish
Naveen Krish 2022-4-3
How should i apply meshgrid? i'm not quite familiar with that. And the documentation i cant able to relate it to my problem

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Image Analyst
Image Analyst 2022-4-3

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