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//Example 16.4
//Finite Difference Method
//Page no. 582
clc;close;clear;
x=0;h=0.25;q=-1;Y(1)=-2;Y(5)=1;
printf('\n i\txi\tYi\tpi\tqi\tri\n-----------------------------------------------\n')
for i=1:5
r(i)=-x^2
if i>1 & i<5 then
printf(' %i\t%g\t%s\t%g\t%i\t%g\n',i-1,x,"?",x,q,r(i))
else
printf(' %i\t%g\t%g\t%g\t%i\t%g\n',i-1,x,Y(i),x,q,r(i))
end
x=x+h
end
x=0;
printf('-----------------------------------------------\n')
for i=1:3
x=x+h
for j=1:3
if i==j then
A(i,j)=2+h^2*q
elseif i<j & abs(i-j)~=2
A(i,j)=-1+h*x/2
elseif i>j & abs(i-j)~=2
A(i,j)=-1-h*x/2
end
end
if i==3 then
B(i)=-h^2*r(i+1)+(-h*x/2+1)*Y(1+2*(i-1))
else
B(i)=-h^2*r(i+1)+(h*x/2+1)*Y(1+2*(i-1))
end
B(i)=(-1)^(i+1)*B(i)
end
disp(B,"B =",A,'A = ')
y=inv(A)*B
for i=1:3
Y(i+1)=y(i)
end
x=0;
disp("The Solution is :",B,"B =",A,'A = ')
printf(' x :')
for i=1:5
printf('\t %.2f',x)
x=x+h
end
x=0;printf('\n y :');
for i=1:5
printf('\t%.3f',Y(i))
end
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