From b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b Mon Sep 17 00:00:00 2001
From: priyanka
Date: Wed, 24 Jun 2015 15:03:17 +0530
Subject: initial commit / add all books

---
 191/CH5/EX5.10/Example5_10.sce | 73 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 73 insertions(+)
 create mode 100755 191/CH5/EX5.10/Example5_10.sce

(limited to '191/CH5/EX5.10/Example5_10.sce')

diff --git a/191/CH5/EX5.10/Example5_10.sce b/191/CH5/EX5.10/Example5_10.sce
new file mode 100755
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+++ b/191/CH5/EX5.10/Example5_10.sce
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+//Illustration cubic spline interpolation with equal difference
+//It needs Symbolic Toolbox
+clc;
+clear;
+close();
+x = -1:1;
+fx = x^4;
+y = fx;
+function y = myfunction(x)
+ y = x^4;
+endfunction
+diff_y = derivative(myfunction, x');
+diff_y0 = diff_y(1);
+diff_y2 = diff_y(9);
+//cd ~/Desktop/maxima_symbolic
+//exec symbolic.sce
+syms a0 b0 c0 d0;
+x = poly(0,'x');
+s0x = a0+b0*x+c0*x^2+d0*x^3;
+syms a1 b1 c1 d1;
+s1x = a1+b1*x+c1*x^2+d1*x^3;
+diff1_s0x = diff(s0x,x);
+diff2_s0x = diff(diff1_s0x,x);
+diff1_s1x = diff(s1x,x);
+diff2_s1x = diff(diff1_s1x,x);
+//from condition(ii)
+x = -1;
+eval(s0x,x);
+//it gives equation a0-b0+c0-d0=1
+x=1;
+eval(s1x,x);
+//it gives equation a1+b1+c1+d1=1
+x = 0;
+eval(s0x,x);
+//it gives equation a0=0
+eval(s1x,x);
+//it gives equation a1=0
+//from condition(iii)
+x=0;
+eval(diff1_s0x,x);
+eval(diff1_s1x,x);
+//it gives b0=b1;
+//from condition(iv)
+eval(diff2_s0x);
+eval(diff2_s1x);
+//it gives 2*c0=2*c1
+//Applying boundary conditions
+x=-1;
+eval(diff1_s0x);
+//it gives b0-2*c0+3*d0=-4
+x=1;
+eval(diff1_s1x);
+//it gives b1+2*c1+3*d1=4
+//Matrix form for the equations
+A=[1 -1 1 -1 0 0 0 0;
+1 0 0 0 0 0 0 0;
+0 0 0 0 1 0 0 0;
+0 0 0 0 1 1 1 1;
+0 1 0 0 0 -1 0 0;
+0 0 1 0 0 0 -1 0;
+0 1 -2 3 0 0 0 0;
+0 0 0 0 0 1 2 3];
+C=[1 0 0 1 0 0 -4 4];
+B = inv(A)*C';
+//it implies
+a0=0;b0=0;c0=-1;d0=-2;a1=0;b1=0;c1=-1;d1=2;
+//for -1<=x<=0
+x=poly(0,'x');
+sx = eval(s0x);
+disp(sx , 'for -1<=x<=0 sx =' );
+//for 0<=x<=1
+sx = eval(s1x);
+disp(sx , 'for 0<=x<=1 sx =' );
\ No newline at end of file
-- 
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