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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 /964/CH4/EX4.2 | |
| 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 '964/CH4/EX4.2')
| -rwxr-xr-x | 964/CH4/EX4.2/4_2.sce | 80 |
1 files changed, 80 insertions, 0 deletions
diff --git a/964/CH4/EX4.2/4_2.sce b/964/CH4/EX4.2/4_2.sce new file mode 100755 index 000000000..9bd0a1887 --- /dev/null +++ b/964/CH4/EX4.2/4_2.sce @@ -0,0 +1,80 @@ +clc;
+clear;
+function y=f(x)
+ y=cos(x)
+endfunction
+xi=%pi/4;
+xf=%pi/3;
+h=xf-xi;
+fi=f(xi);//function value at xi
+ffa=f(xf);//actual function value at xf
+
+//for n=0, i.e, zero order approximation
+ff=fi;
+et(1)=(ffa-ff)*100/ffa;//percent relative error at x=1
+disp(ff,"The value of f at x=1 due to zero order approximation :")
+disp(et(1),"% relative error :")
+disp("----------------------------------------------")
+
+//for n=1, i.e, first order approximation
+deff('y=f1(x)','y=derivative(f,x,order=4)')
+f1i=f1(xi);//value of first derivative of function at xi
+f1f=fi+f1i*h;//value of first derivative of function at xf
+et(2)=(ffa-f1f)*100/ffa;//% relative error at x=1
+disp(f1f,"The value of f at x=1 due to first order approximation :")
+disp(et(2),"% relative error :")
+disp("----------------------------------------------")
+
+
+//for n=2, i.e, second order approximation
+deff('y=f2(x)','y=derivative(f1,x,order=4)')
+f2i=f2(xi);//value of second derivative of function at xi
+f2f=f1f+f2i*(h^2)/factorial(2);//value of second derivative of function at xf
+et(3)=(ffa-f2f)*100/ffa;//% relative error at x=1
+disp(f2f,"The value of f at x=1 due to second order approximation :")
+disp(et(3),"% relative error :")
+disp("----------------------------------------------")
+
+
+//for n=3, i.e, third order approximation
+deff('y=f3(x)','y=derivative(f2,x,order=4)')
+f3i=f3(xi);//value of third derivative of function at xi
+f3f=f2f+f3i*(h^3)/factorial(3);//value of third derivative of function at xf
+et(4)=(ffa-f3f)*100/ffa;//% relative error at x=1
+disp(f3f,"The value of f at x=1 due to third order approximation :")
+disp(et(4),"% relative error :")
+disp("----------------------------------------------")
+
+
+//for n=4, i.e, fourth order approximation
+deff('y=f4(x)','y=derivative(f3,x,order=4)')
+f4i=f4(xi);//value of fourth derivative of function at xi
+f4f=f3f+f4i*(h^4)/factorial(4);//value of fourth derivative of function at xf
+et(5)=(ffa-f4f)*100/ffa;//% relative error at x=1
+disp(f4f,"The value of f at x=1 due to fourth order approximation :")
+disp(et(5),"% relative error :")
+disp("----------------------------------------------")
+
+
+//for n=5, i.e, fifth order approximation
+f5i=(f4(1.1*xi)-f4(0.9*xi))/(2*0.1);//value of fifth derivative of function at xi (central difference method)
+f5f=f4f+f5i*(h^5)/factorial(5);//value of fifth derivative of function at xf
+et(6)=(ffa-f5f)*100/ffa;//% relative error at x=1
+disp(f5f,"The value of f at x=1 due to fifth order approximation :")
+disp(et(6),"% relative error :")
+disp("----------------------------------------------")
+
+
+//for n=6, i.e, sixth order approximation
+deff('y=f6(x)','y=derivative(f5,x,order=4)')
+f6i=(f4(1.1*xi)-2*f4(xi)+f4(0.9*xi))/(0.1^2);//value of sixth derivative of function at xi (central difference method)
+f6f=f5f+f6i*(h^6)/factorial(6);//value of sixth derivative of function at xf
+et(6)=(ffa-f6f)*100/ffa;//% relative error at x=1
+disp(f6f,"The value of f at x=1 due to sixth order approximation :")
+disp(et(6),"% relative error :")
+disp("----------------------------------------------")
+
+
+
+
+
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