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//Example 20.5
//Nine Point Formula
//Page no. 688
clc;clear;close;
printf('Itr\t\t U11\t\t U12\t\t U21\t\t U22\n-----------------------------------------------------------------------\n')
for i=1:4
for j=1:4
if j==1 then
u(i,j)=0
elseif j==4
u(i,j)=100
elseif (i==1 | i==4) & j==2
u(i,j)=25
elseif i==1 | i==4
u(i,j)=u(i,j-1)*2
else
u(i,j)=0
end
end
end
for k=0:17
printf(' %i\t\t%.3f\t\t%.3f\t\t%.3f\t\t%.3f\n',k,u(3,2),u(2,2),u(3,3),u(2,3))
for i=3:-1:2
for j=2:3
u1(i,j)=(u(i+1,j-1)+u(i-1,j-1)+u(i+1,j+1)+u(i-1,j+1)+4*(u(i,j+1)+u(i,j-1)+u(i-1,j)+u(i+1,j)))/20
end
end
for i=3:-1:2
for j=2:3
u(i,j)=u1(i,j)
end
end
end
disp(u,'The Solution of the System is = ')
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