Finite Difference Method Boundary Value Problem

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Lingbai Ren 2021-11-10

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https://ww2.mathworks.cn/matlabcentral/answers/1583154-finite-difference-method-boundary-value-problem

评论： Jan 2021-11-11

Hi, I am lost in this Boundary Value Problem requiring to use Finite Difference Method:

I attached what I have done and the hint our professor provided, I also tried different methods from other matlab questions and youtube, but it always runs some error.

Below this is the code I hae so far, it works but it does not look correct, can anyone help please? I will really appreciate that!

%% Initialize parameters
clc,clear
T_B = 600; % boundary condition
T_E = 350; % boundary condition
T_Inf = 300;
M = 4;
L = 2.0;
% Discretization
num_nodes = 51;
num_segments = num_nodes-1;
h = L/num_segments;
% x = T_B:-h:T_E;
xj = 0:h:L;
Q=@(T)(-4*(300-T));
% Building up matrix
diagonal = [1/h; 2/h^2*ones(num_segments-1,1); 1/h];
A = diag( diagonal);
for i = 2:num_segments+1
    A(i-1,i)=-1/h^2; A(i,i-1)=-1/h^2;  %%%%%%%%%%%%%%  signs
end
A(1,2)=0; A(num_segments+1,num_segments)=0;
b = [T_B/h; Q(xj(2:end-1))'; T_E/h];  %%%%%%%%%%%%%%% Q(xj(2_end-1))' not just Q
T=A\b;
plot(xj,T),grid

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Lingbai Ren 2021-11-10

plot.jpg

Sorry, this is the plot I get

Jan 2021-11-11

This does not clarify, wh yozu assume, that there is a problem. Remember, that the readers are not working in your field. So explain the problem like you would explain it to a rubber duck.

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