Question

For a function, only the numerical values are available as shown in the table bellow, Write a MATLAB script file to calculate the derivative of y, use a ‘for loop’ to apply the centered method to the middle 8 points. Hint: Define x and y as arrays, so you can easily call them in formula and the for loop

xi = 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

yi = 1.815 2.16 2.535 2.94 3.375 3.84 4.335 4.86 5.415 6

Answer 1

Answer:----

Given,

xi = 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

yi = 1.815 2.16 2.535 2.94 3.375 3.84 4.335 4.86 5.415 6

MATLAB script file to calculate the derivative of y, use a ‘for loop’ to apply the centered method to the middle 8 points

Here the code is

%Define function

function ff= forward(yi,xi,p)

%Find value

ff= (yi(p + 1) - yi(p)) / (xi(p + 1) - xi(p));

%End

end

%Define function

function bb= backward(yi,xi,p)

%Find value

bb = (yi(p) - yi(p - 1)) / (xi(p) - xi(p - 1));

%End

end

%Define function

function cc= central(yi, xi, p)

%Find value

cc = (yi(p + 1) - yi(p - 1)) / (xi(p + 1) - xi(p - 1));

%End

end

%Define xi

xi=[1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0];

%Define yi

yi=[1.815 2.16 2.535 2.94 3.375 3.84 4.335 4.86 5.415 6];

%Define value

size =10;

%Define value

di=zeros(size,1);

%Call Function

di(1) = forward(yi, xi, 1);

%Loop

for n = 2:size-1

%Call Function

di(n) = central(yi, xi, n);

end

%Call Function

di(size) = backward(yi, xi, size);

%Display message

fprintf('\n %s   %s %s','xi', 'yi', 'Derivative');

%For loop

for n=1:10

%Display message

fprintf('\n %.2f %.3f %.3f',xi(n), yi(n), di(n));

%End

end

The sample output :---