Array indices must be positive integers or logical values Error

The question I am trying to answer is: Write a program to test the two finite difference approximations in section 1.6 (the forward and centered difference formulas). Test your program on the function arctan(x) at x=sqrt(2).Start with h = 1/2, and generate a sequence of approximations by reducing h by a factor of 2 each time, until h = 2−40. Observe how the error changes with h.

So far I have;

f(x)=atan(x);
x=sqrt(2) ; 
h=1:.5:2^(-40);

%Forward Euler
F(x)=((f(x+h)-f(x))/h);

I keep getting the array indices must be positive integers or logical values error.

[Adam]

f(x)=atan(x);

What are you looking to do with this line? f will be an array here and x the index into it. You haven't defined x before this line though immediately afterwards you define it to sqrt(2) which clearly is not an integer to use as an index.

Are you expecting the above line to define a function? If so you would need it to be more like

f = @(x) atan( x );

[Abigail Mullen]

I suppose I am just not sure how to do this problem, thank you for your help - I am new to matlab.

Answer 1

[Ashutosh Prasad]

The error that you are getting is because of the way you are defining the h vector. Your definition creates an empty vector with no elements. But I understand you want h to be halved on each iteration, that's when loops come handy.

Try execution the following script

 f = @(x) atan(x);
 x = sqrt(2) ; 
 h = 0.5;
 %Forward Euler
 while(h >= 2^(-40))
   F = ((f(x+h)-f(x))/h);
   h = h/2;
 end

Let me know if this helps