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//Example 10.5
clc
clear
x = 0:4;
y = 0:4;
m = length(y);
n = length(x);
u = zeros(m,n);
u(m,:) = x.^3;
u(:,n) = 16*y';
u0 = u;
I = ceil(m/2);
J = ceil(n/2);
u(J,I) = (u0(J-2,I-2) + u0(J-2,I+2) + u0(J+2,I-2) + u0(J+2,I+2)) / 4;
for j = [J-1 J+1]
for i = [I-1 I+1]
u(j,i) = (u(j-1,i-1) + u(j-1,i+1) + u(j+1,i-1) + u(j+1,i+1)) / 4;
end
end
j1 = [J-1 J J J+1];
i1 = [I I-1 I+1 I];
for k = 1:4
i = i1(k);
j = j1(k);
u(j,i) = (u(j,i-1) + u(j,i+1) + u(j-1,i) + u(j+1,i)) / 4;
end
disp(u,"u:")
p = m-1;
q = n-1;
c = cos(%pi/p) + cos(%pi/q);
w = 4/(2+sqrt(4-c^2));
w = round(w*10^3)/10^3;
kf = 10;
tab = zeros(kf+1,(m-2)*(n-2));
row = [];
for j = 2:n-1
row = [row u(j,2:m-1)];
end
tab(1,:) = row;
for k = 1:kf
row = [];
for j = 2:n-1
for i = 2:m-1
u(j,i) = (u(j,i-1) + u(j,i+1) + u(j-1,i) + u(j+1,i)) *w/4 + (1-w)*u(j,i);
end
row = [row u(j,2:m-1)];
end
row = round(row*10^4)/10^4;
tab(k+1,:) = row;
end
mprintf("\n\n%8s %9s %10s %10s %9s %10s %10s %9s %9s",'u11','u21','u31','u12','u22','u32','u13','u23','u33')
disp(tab)
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