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);