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| author | priyanka | 2015-06-24 15:03:17 +0530 |
|---|---|---|
| committer | priyanka | 2015-06-24 15:03:17 +0530 |
| commit | b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (patch) | |
| tree | ab291cffc65280e58ac82470ba63fbcca7805165 /191/CH5/EX5.11 | |
| download | Scilab-TBC-Uploads-b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b.tar.gz Scilab-TBC-Uploads-b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b.tar.bz2 Scilab-TBC-Uploads-b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b.zip | |
initial commit / add all books
Diffstat (limited to '191/CH5/EX5.11')
| -rwxr-xr-x | 191/CH5/EX5.11/Example5_11.sce | 46 | ||||
| -rwxr-xr-x | 191/CH5/EX5.11/Result5_11.txt | 6 |
2 files changed, 52 insertions, 0 deletions
diff --git a/191/CH5/EX5.11/Example5_11.sce b/191/CH5/EX5.11/Example5_11.sce new file mode 100755 index 000000000..31dc3d3ab --- /dev/null +++ b/191/CH5/EX5.11/Example5_11.sce @@ -0,0 +1,46 @@ +//Illustration cubic spline interpolation with unequal difference
+clc;
+clear;
+close();
+//with free boundary conditions
+xi = [0 1 3 3.5 5];
+yi = [1.00000 0.54030 -0.98999 -0.93646 0.28366];
+n = 4;
+h0 = xi(2)-xi(1);
+h1 = xi(3)-xi(2);
+h2 = xi(4)-xi(3);
+h3 = xi(5)-xi(4);
+//After imposing free boundary conditions the matrix we get
+A = [2 1 0 0 0;
+1 3 1/2 0 0;
+0 1/2 5 2 0;
+0 0 2 16/3 2/3;
+0 0 0 2/3 4/3];
+C = [-1.37910 ; -2.52682 ; -0.50536 ; 2.26919 ; 1.62683] ;
+format('v',8);
+B = inv(A)*C;
+//it gives
+diff1_y0 = -0.33966;
+diff1_y1 = -0.69978;
+diff1_y2 = -0.17566;
+diff1_y3 = 0.36142;
+diff1_y4 = 1.03941;
+//cubic polynomial for 3<=x<=3.5
+x = poly(0,'x')
+s2x = yi(3)*[{(x-3.5)*(x-3.5)/(0.5*0.5)}+{2*(x-3)*(x-3.5)*(x-3.5)/(0.5*0.5*0.5)}] + yi(4)*[{(x-3)*(x-3)/(0.5*0.5)}-{2*(x-3.5)*(x-3)*(x-3)/(0.5*0.5*0.5)}] + diff1_y2*{(x-3)*(x-3.5)*(x-3.5)/(0.5*0.5)} + diff1_y3*{(x-3.5)*(x-3)*(x-3)/(0.5*0.5)};
+x = 3.14159;
+disp(horner(s2x,x) , 'value of s2x at 3.14159 : ');
+//with clamped boundary conditions
+diff1_y0 = -sin(0);
+diff1_y4 = -sin(5);
+//matrix form
+A = [3 0.5 0;0.5 5 2 ; 0 2 16/3];
+C = [-2.52682 ; -0.50536 ; 1.62991];
+B = inv(A)*C;
+//it gives
+diff1_y1 = -0.81446;
+diff1_y2 = -0.16691;
+diff1_y3 = 0.36820;
+s2x = yi(3)*[{(x-3.5)*(x-3.5)/(0.5*0.5)}+{2*(x-3)*(x-3.5)*(x-3.5)/(0.5*0.5*0.5)}] + yi(4)*[{(x-3)*(x-3)/(0.5*0.5)}-{2*(x-3.5)*(x-3)*(x-3)/(0.5*0.5*0.5)}] + diff1_y2*{(x-3)*(x-3.5)*(x-3.5)/(0.5*0.5)} + diff1_y3*{(x-3.5)*(x-3)*(x-3)/(0.5*0.5)};
+x = 3.14159;
+disp(horner(s2x,x) , 'value of s2x at 3.14159 : ');
\ No newline at end of file diff --git a/191/CH5/EX5.11/Result5_11.txt b/191/CH5/EX5.11/Result5_11.txt new file mode 100755 index 000000000..88c611365 --- /dev/null +++ b/191/CH5/EX5.11/Result5_11.txt @@ -0,0 +1,6 @@ + value of s2x at 3.14159 :
+
+ - 1.00271
+value of s2x at 3.14159 :
+
+ - 1.00227
\ No newline at end of file |