1D transient heat equation

I am trying to solve this matrix: T=[A]^-1[B]. Initially the temperature is at 80C, but changes as time increases. The change in time is 30 seconds and the number of iterations I want to code for is 120. The current code I have does not work. Somehow I need some guidance how how to update the matrix inside the for loop and display for T(1)-T(10).

n=120; %number of iterations

t=0; %initial time

dt=30; %change in time [seconds]

tmax = 3600; %cool for 1 hr

T_initial = [80; 80; 80; 80; 80; 80; 80; 80; 80; 80; 80]; %initial temperature

A=[-230,50,0,0,0,0,0,0,0,0,0;

50,-460,50,0,0,0,0,0,0,0,0;

0,50,-460,50,0,0,0,0,0,0,0;

0,0,50,-460,50,0,0,0,0,0,0;

0,0,0,50,-460,50,0,0,0,0,0;

0,0,0,0,50,-460,50,0,0,0,0;

0,0,0,0,0,50,-460,50,0,0,0;

0,0,0,0,0,0,50,-460,50,0,0;

0,0,0,0,0,0,0,50,-460,50,0;

0,0,0,0,0,0,0,0,50,-460,50;

0,0,0,0,0,0,0,0,0,50,-330];

B =[-14400;-28800;-28800;-28800;-28800;-28800;-28800;-28800;-28800;-28800;-16400];

for i=1 %initialize solution

T(i)=T_initial;

end

T(1)=T_initial;

while (t < tmax)

i=i+1;

t=t+dt;

for i=2:n-1

T(i) = A\B;

end

end

Answer 1

[Wilmer Alexander - Conferencista en Automatización y Robótica más influyente en Iberoamérica]

clc
clear
A=[-230,50,0,0,0,0,0,0,0,0,0;
    50,-460,50,0,0,0,0,0,0,0,0;
    0,50,-460,50,0,0,0,0,0,0,0;
    0,0,50,-460,50,0,0,0,0,0,0;
    0,0,0,50,-460,50,0,0,0,0,0;
    0,0,0,0,50,-460,50,0,0,0,0;
    0,0,0,0,0,50,-460,50,0,0,0;
    0,0,0,0,0,0,50,-460,50,0,0;
    0,0,0,0,0,0,0,50,-460,50,0;
    0,0,0,0,0,0,0,0,50,-460,50;
    0,0,0,0,0,0,0,0,0,50,-330];
B =[-14400;-28800;-28800;-28800;-28800;-28800;-28800;-28800;-28800;-28800;-16400];
T=A\B 

[Wilmer Alexander - Conferencista en Automatización y Robótica más influyente en Iberoamérica]

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