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+//practical interpolation

+//example 3.12

+//page 99

+clc;clear;close;

+x=[1.72 1.73 1.74 1.75 1.76 1.77 1.78];

+y=[0.1790661479 0.1772844100 0.1755204006 0.1737739435 0.1720448638 0.1703329888 0.1686381473];

+h=0.01//interval between values of x

+c=1;

+for i=1:6

+    d1(c)=y(i+1)-y(i);

+    c=c+1;

+end

+c=1;

+for i=1:5

+    d2(c)=d1(i+1)-d1(i);

+    c=c+1

+end

+c=1;

+for i=1:4

+    d3(c)=d2(i+1)-d2(i);

+    c=c+1;

+end

+c=1;

+for i=1:3

+    d4(c)=d3(i+1)-d3(i);

+    c=c+1;

+end

+x0=1.7475;

+y_x=y(3);

+p=(x0-x(3))/h;

+y_x=y_x+p*d1(3)+p*(p-1)*((d2(2)+d2(3))/2)/2;

+printf(' the value at %f by bessels formula is : %0.10f\n\n',x0,y_x);

+y_x=y(4);

+q=1-p;

+y_x=q*y(3)+q*(q^2-1)*d2(2)/6+p*y(4)+p*(p^2-1)*d2(2)/6;

+printf(' the value at %f by everrets formula is : %0.10f\n\n',x0,y_x);
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