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+//Example 5.51

+//Spline Interpolation

+//Page no. 204

+clc;close;clear;

+

+xi=[1,2,3];

+yi=[-6,-1,16];

+h=1;n=2;

+x=poly(0,'x')

+m(2)=(6*(yi(3)-2*yi(2)+yi(1)))/4

+m(1)=0;m(3)=0;

+function [y]=S(i,x)

+    y=m(i)*(xi(i+1)-x)^3/(6*h)

+    y=y+m(i+1)*(x-xi(i))^3/(6*h)

+    y=y+(yi(i)/h-(m(i)*h)/6)*(xi(i+1)-x)

+    y=y+(yi(i+1)/h-(m(i+1)*h)/6)*(-xi(i)+x)

+endfunction

+for i=1:2

+    S1(i)=S(i);

+end

+printf('\n The required Spline is : \n')

+disp(' ','2<x<=3',S1(2),'S2 = ',' ','1<=x<=2',S1(1),'S1 = ');

+x=1.5;

+if x>=1 & x<=2 then

+    i=1;

+else x>2 & x<=3

+    i=2;

+end

+disp(S(i,x),'y(1.5) = ')

+x=2;h1=0.01;

+for i=1:2

+   Sd(i,x)=(S(i,x+h1)-S(i,x))/h1 

+end

+disp(Sd(2,2),Sd(1,2),'y`(2) = ')
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