clearvars
clc
f=@(x)-exp(-5*x)*(9975*sin(100*x)+1000*cos(100*x));
% parameters
nx=91;
L=1;
dx=L/(nx-1);
h=dx;
x=linspace(0,L,nx);
%Boundary conditions
u(1,:)=0;
u(nx,:)=0;
% Multiquadric RBF
beta=20;
a=beta*h;
% Define G(x)
G=zeros(nx,nx+2);
for j=1:nx
for i=1:nx
G(i,j)=sqrt((x(i)-x(j))^2+a^2);
end
end
% Extract the first and last rows of the matrix G
G1=G(1,:);
G2=G(end,:);
G_bar=[G1;G2];
G_a=G(2:end-1,:);
%H
H=zeros(nx,nx);
for i=1:nx
for j=1:nx
H(i,j)=(((x(i)-x(j))*sqrt((x(i)-x(j)).^2+a.^2))/2)+((a.^2)/2)*...
log((x(i)-x(j))+sqrt((x(i)-x(j)).^2+a.^2));
end
end
H_a=[H,ones(nx,1),zeros(nx,1)];
% Plot H
% surf(x, x, H); % 3D plot of H
% xlabel('x');
% ylabel('x');
% zlabel('H');
% title('Plot of H');
% colorbar;
% hold on
%H_bar
H1=zeros(nx,nx);
for i=1:nx
for j=1:nx
H1(i,j)=((sqrt((x(i)-x(j)).^2+a.^2))/6)+((a.^2)/2)*(x(i)-x(j))*....
log((x(i)-x(j))+sqrt((x(i)-x(j)).^2+a.^2))-((a.^2)/2)*...
sqrt((x(i)-x(j)).^2+a.^2);
end
end
% 3D plot of H1
% surf(x, x, H1);
% xlabel('x');
% ylabel('x');
% zlabel('H1');
% title('Plot of H1');
% colorbar;
% Add the new column x and 1
H_bar=[H1,x',ones(size(H,1),1)];
H_inv=pinv(H_bar);
% Conversion matrix
C=[H_bar;G_bar];
C_inv=pinv(C);
%f
f_1=f(0);
f_nx=f(x(nx));
D=[u;f_1;f_nx];
E=C_inv*D;
f_interior=G_a*E;
%A
A=zeros(nx-2,nx-2);
% Populate the tri-diagonal structure of A
for i=2:nx-1
A(i-1,i-1)=-2*exp(-5*x(i))*(9975*sin(100*x(i))+1000*cos(100*x(i)));
if i>2
A(i-1,i-2)=exp(-5*x(i-1))*(9975*sin(100*x(i-1))+1000*cos(100*x(i-1)));
end
if i
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