Question

solve using MATLAB.
Title: Numerical differentiations.

Use Richardson extrapolation to estimate the first derivative of y = cos x at x = π/4 using step sizes of h₁ = π/3 and h₂ = π/6. Employ centered differences of O(h²) for the initial estimates.

solve using MATLAB.

Answer 1

%%Matlab code for Richardson Extrapolation
clear all
close all

%function for which differentiation have to do
f=@(x) cos(x) ;
x=pi/4;
h1=pi/3; h2=pi/6;

%differetiation using central difference
df1=(f(x+h1)-f(x-h1))/(2*h1);
df2=(f(x+h2)-f(x-h2))/(2*h2);

fprintf('\tExact differential at x=pi/4 is %f\n',-sin(x));

fprintf('\tCentral difference for h1=%f is %f\n',h1,df1)

fprintf('\tCentral difference for h2=%f is %f\n',h2,df2)

dff=df2+((df2-df1)/3);

fprintf('\tRichardson extrapolation at x=%f is %f\n',pi/4,dff)

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