1 files changed, 65 insertions, 0 deletions
diff --git a/964/CH4/EX4.1/4_1.sce b/964/CH4/EX4.1/4_1.sce
new file mode 100755
index 000000000..146a0dcb6
--- /dev/null
+++ b/964/CH4/EX4.1/4_1.sce
@@ -0,0 +1,65 @@
+clc;
+clear;
+function y=f(x)
+    y=-0.1*x^4-0.15*x^3-0.5*x^2-0.25*x+1.2;
+endfunction
+xi=0;
+xf=1;
+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;//truncation error at x=1
+disp(fi,"The value of f at x=0 :")
+disp(ff,"The value of f at x=1 due to zero order approximation :")
+disp(Et(1),"Truncation 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;//truncation error at x=1
+disp(f1i,"The value of first derivative of f at x=0 :")
+disp(f1f,"The value of f at x=1 due to first order approximation :")
+disp(Et(2),"Truncation 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;//truncation error at x=1
+disp(f2i,"The value of second derivative of f at x=0 :")
+disp(f2f,"The value of f at x=1 due to second order approximation :")
+disp(Et(3),"Truncation 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;//truncation error at x=1
+disp(f3i,"The value of third derivative of f at x=0 :")
+disp(f3f,"The value of f at x=1 due to third order approximation :")
+disp(Et(4),"Truncation 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;//truncation error at x=1
+disp(f4i,"The value of fourth derivative of f at x=0 :")
+disp(f4f,"The value of f at x=1 due to fourth order approximation :")
+disp(Et(5),"Truncation error :")
+disp("----------------------------------------------")
+
+
+
+
+
+