error in for loop

We want to fix the problem of the for loop in the code below without changing the boundary conditions. What is your suggestion? Thank you in advance.

clc;
clear;
close all;

R = linspace(-10, 10, 12);
h = 1e-3;
u_values = zeros(1, length(R));  % Array to store u values

% Calculate u for all R values
for j = 1:length(R)
    u = (4 * R(j).^5) - (6 * R(j).^3);  % Calculate u for current R
    u_values(j) = u;  % Store u value
    fprintf('u for R = %.2f: %f\n', R(j), u);
    if j==1
        derivative = (1/(60*h) * (u(j+3) - u(j-3))) - (3/(20*h) * (u(j+2) - u(j-2))) + (3/(4*h) * (u(j+1) - u(j-1)));
    end
end

u for R = -10.00: -394000.000000

Index exceeds the number of array elements. Index must not exceed 1.

this error:

Index exceeds the number of array elements (1).

Error in Untitled2 (line 17)

derivative = (1/(60*h) * (u(j+1) - u(j-1))) - (3/(20*h) * (u(j) - u(j-2))) + (3/(4*h) * (u(j) - u(j-1)));

Answer 1

[Torsten]

u(j-3) is only defined for j>=4, u(j+3) is only defined for j<=length(R)-3. Similar restrictions hold for the other indices. Thus your loop must start with j = 4 and end with length(R)-3.

[Walter Roberson]

    if j==1
        derivative = (1/(60*h) * (u(j+3) - u(j-3))) - (3/(20*h) * (u(j+2) - u(j-2))) + (3/(4*h) * (u(j+1) - u(j-1)));
        

If you start the loop at j = 4, then j==1 will never be true, so the derivative would never be calculated.

[Torsten]

ok, I correct:

Thus your loop must start with j = 4, end with length(R)-3 and you can remove the if-statement.

Further, the vector u must be defined before entering the loop.

R = linspace(-10, 10, 120);
h = R(2)-R(1);
u = 4 * R.^5 - 6 * R.^3;
derivative = nan(size(u));
for j = 4:length(R)-3
    derivative(j) = (1/(60*h) * (u(j+3) - u(j-3))) - (3/(20*h) * (u(j+2) - u(j-2))) + (3/(4*h) * (u(j+1) - u(j-1)));
end
hold on
plot(R,derivative)
plot(R,20*R.^4-18*R.^2,'o')
hold off
grid on

If you need derivatives nearer to the boundaries, you will have to use a method of lower order that uses a smaller stencil.