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//Example 5.20
//Newtons Forward Difference Formula
//Page no. 144
clc;close;clear;
printf(' x\t sin x\t\t 1st\t\t 2nd\t\t 3rd\t\t 4th\t\t 5th\n\t\t\tdifference\tdifference\tdifference\tdifference\tdifference\t')
printf('\n---------------------------------------------------------------------------------------------------')
h=0.2;
z=[0.5,0.47943;0.7,0.64422;0.9,0.78333;1.1,0.89121;1.3,0.96356;1.5,0.99749]
deff('y=f(x,p)','y=z(x,2)+p*z(x,3)+p*(p+1)*z(x,4)/2+p*(p+1)*(p+2)*z(x,5)/6+p*(p+1)*(p+2)*(p+3)*z(x,6)/24')
deff('y=f1(x,p)','y=z(x,2)+p*z(x,3)+p*(p-1)*z(x,4)/2+p*(p-1)*(p-2)*z(x,5)/6+p*(p-1)*(p-2)*(p-3)*z(x,6)/24+p*(p-1)*(p-2)*(p-3)*(p-4)*z(x,7)/120')
x01=0.5;x11=0.54;
x02=1.3;x12=1.36
for i=3:7
for j=1:8-i
z(j,i)=z(j+1,i-1)-z(j,i-1)
end
end
printf('\n')
for i=1:6
for j=1:7
if z(i,j)==0 then
printf(' \t')
else
if j==1 then
printf(' %.1f\t',z(i,j))
else
printf('%.7f\t',z(i,j))
end
end
end
printf('\n')
end
p=(x11-x01)/h;
disp(f1(1,p),"fp (0.54) =");
p=(x12-x02)/h;
disp(f(5,p),"fp (1.36) =");
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