Having all the codes in a single file

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Pouyan Msgn 2021-3-28

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https://ww2.mathworks.cn/matlabcentral/answers/785791-having-all-the-codes-in-a-single-file

评论： Jan 2021-3-29

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I saw an example of boundary value problems in the book Numerical Analysis by Sauer. We have the non-linear equation:

The discretized form of this equation :

My question is not about how we solve such a problem. I already have the solution in three files. Ie two functions and a regular matlab file to perform it. I also attached files.I tried to write everything in a single file and wanted to see if it is possible to execute the algorithm without having to write Matlab functions. I did not succeed. Can anyone correct my code?

clc
clear all
n=15;
a=0; b=1; ya=1; yb=4;
h=(b-a)/(n+1);
J=zeros(n,n); %Jacobian
w=zeros(n,1);
y=zeros(n,1);
y(1)=ya-(2+h^2)*w(1)+h^2*w(1)^2+w(2); %BV
y(n)=w(n-1)-(2+h^2)*w(n)+(h^2)*(w(n)^2)+yb; %BV
for i=2:n-1
    y(i)=w(i-1)-(2+h^2)*w(i)+(h^2)*(w(i)^2)+w(i+1);
end
for i=1:n-1
    J(i,i+1)=1;
    J(i+1,i)=1;
end
%The Matrix
for i=1:n
    J(i,i)=2*h^2*w(i)-2-h^2;
end
%The solution!
w=w-J\y;
Y=[1;w;4];
plot(x,Y)
grid on