Solving Numerical Differentiation Problem using Scilab Programming
Given f(x)=exp(-x^2), find f'(x).
In this video, solution to differentiation problem using D1 dan D2 formula and the best estimation using extrapolation.
The computation is shown using Scilab.
I recorded this video during my lecture so you can hear me speaking Bahasa Melayu and English.
The full code is given here.
// This code performs NUMERICAL DIFFERENTIATION
// The name of this function file is f.sci
function y=f(x)
y=exp(-x^2);
endfunction
// The name of this function file is D1.sci
// This is D1 formula
function d1=D1(x,h)
d1=(f(x+h)-f(x))/h;
endfunction
// The name of this function file is D2.sci
// This is D2 formula
function y=D2(x,h)
y=(f(x+h)-f(x-h))/(2*h);
endfunction
x=1;
h=0.2;
disp("The D1 approximation is:")
y1=D1(x,h);
disp(y1);
disp("The D2 approximation is:")
y2=D2(x,h);
disp(y2);
// Extrapolation
T11=2(x,h); //h
T21=D2(x,h/2); // h/2
T31=D2(x,h/4); // h/4
T22=(4*T21-T11)/3;
T32=(4*T31-T21)/3;
T33=(16*T32-T22)/15;
disp("The best approximation using h/2 and h is")
disp(T22)
disp("The best approximation using h/4, h/2 and h is")
disp(T33)
// Exact Solution
function yp=exact(x)
yp=-2*x*exp(-x^2); // EXACT FOR y=exp(-x^2)
endfunction
// Finding the numerical errors
E1=abs(exact(x)-T22);
E2=abs(exact(x)-T33);
disp("The error for T22 is: ")
disp(E1);
disp("The error for T33 is: ")
disp(E2);
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