1. Sajid Ali
081220-097
INTERPOLATION Methods:
NEWTON FORWARD DIFFERENCE METHOD:
n = input('nEnter number of data points = ');
h = input('nEnter step size (h) = ')
x(1) = input('nx0 = ');
y(1) = input('y0 = ');
for i=2:n
x(i)=x(i-1)+h;
fprintf('nX%d = %f',i,x(i));
fprintf('ttY%d: ',i);
y(i) = input('');
end
x_reqd = input('nEnter X for which value of Y is sought: ');
s=(x_reqd-x(1))/h;
for i=1:n
diff(i,1)=y(i);
end
%% Calculate Forward Differance Table
for j=2:n
for i=1:n-j+1
diff(i,j)=diff(i+1,j-1)-diff(i,j-1);
end
end
%% Print Forward Differance Table
fprintf('ntXt Forward Differance Table');
for i=1:n
fprintf('n %.4f',x(i));
for j=1:n-i+1
fprintf('t%.4f',diff(i,j));
end
end
ans=y(1);
for i=1:n-1
term=1;
for j=1:i
term=term*(s+j-1)/j;
end
ans=ans+term*diff(1,i+1);
end
Backward Methed:
function Forward()
x=[0;1;2;3;4;5;6];

2. y=[2;3;10;29;66;127;218];
dy=[y(2,1)-y(1,1);y(3,1)-y(2,1);y(4,1)-y(3,1);y(5,1)-y(4,1);y(6,1)-
y(5,1);y(7,1)-y(6,1)];
d2y=[dy(2,1)-dy(1,1);dy(3,1)-dy(2,1);dy(4,1)-dy(3,1);dy(5,1)-
dy(4,1);dy(6,1)-dy(5,1)];
d3y=[d2y(2,1)-d2y(1,1);d2y(3,1)-d2y(2,1);d2y(4,1)-d2y(3,1);d2y(5,1)-
d2y(4,1)];
d4y=[d3y(2,1)-d3y(1,1);d3y(3,1)-d3y(2,1);d3y(4,1)-d3y(3,1)];
d5y=[d4y(2,1)-d4y(1,1);d4y(3,1)-d4y(2,1)];
d6y=[d5y(2,1)-d5y(1,1)];
p=(.5-0)/1;
Y=y(1,1)+(((p*dy(1,1)))+((p*(p-1))/2)*d2y(1,1))+(((p*(p-1)*(p-
2))/6)*d3y(1,1))+(((p*(p-1)*(p-2)*(p-3))/24)*d4y(1,1))+(((p*(p-1)*(p-2)*(p-
3)*(p-4))/120)*d5y(1,1))+(((p*(p-1)*(p-2)*(p-3)*(p-4)*(p-5))/720)*d6y(1,1))
end
Striling
function Forward()
x=[0;1;2;3;4;5;6];
y=[2;3;10;29;66;127;218];
dy=[y(2,1)-y(1,1);y(3,1)-y(2,1);y(4,1)-y(3,1);y(5,1)-y(4,1);y(6,1)-
y(5,1);y(7,1)-y(6,1)];
d2y=[dy(2,1)-dy(1,1);dy(3,1)-dy(2,1);dy(4,1)-dy(3,1);dy(5,1)-
dy(4,1);dy(6,1)-dy(5,1)];
d3y=[d2y(2,1)-d2y(1,1);d2y(3,1)-d2y(2,1);d2y(4,1)-d2y(3,1);d2y(5,1)-
d2y(4,1)];
d4y=[d3y(2,1)-d3y(1,1);d3y(3,1)-d3y(2,1);d3y(4,1)-d3y(3,1)];
d5y=[d4y(2,1)-d4y(1,1);d4y(3,1)-d4y(2,1)];
d6y=[d5y(2,1)-d5y(1,1)];
p=(.5-0)/1;
Y=y(1,1)+(((p*dy(1,1)))+((p*(p-1))/2)*d2y(1,1))+(((p*(p-1)*(p-
2))/6)*d3y(1,1))+(((p*(p-1)*(p-2)*(p-3))/24)*d4y(1,1))+(((p*(p-1)*(p-
2)*(p-3)*(p-4))/120)*d5y(1,1))+(((p*(p-1)*(p-2)*(p-3)*(p-4)*(p-
5))/720)*d6y(1,1))
end