Unrecognized function or variable 'TrapComp'

Hello, every time i run this code it returns (Unrecognized function or variable 'TrapComp'.),

please help me,

function I = Romberg(f,a,b,n,n_levels)
%
% Romberg uses the Romberg integration scheme to find
% integral estimates at different levels of accuracy.
%
% I = Romberg(f,a,b,n,n_levels) where
%
% f is an inline function representing the integrand,
% a and b are the limits of integration,
% n is the initial number of equal-length
% subintervals in [a,b],
% n_levels is the number of accuracy levels,
%
% I is the matrix of integral estimates.
%
I = zeros(n_levels,n_levels); % Pre-allocate
% Calculate the first-column entries by using the
% composite trapezoidal rule, where the number of
% subintervals is doubled going from one element
% to the next.
for i = 1:n_levels,
n_intervals = 2^(i-1)*n;
I(i,1) = TrapComp(f,a,b,n_intervals);
end
% Starting with the second level, use Romberg scheme to
% generate the remaining entries of the table.
for j = 2:n_levels
for i = 1:n_levels - j+1,
I(i,j) = (4^(j-1)*I(i+1,j-1)-I(i,j-1))/(4^(j-1)-1);
end
end

[Star Strider]

I cannot locate anything like that in a File Exchange search. You need to go back to wherever you downloaded that file and download all the associated functions with it, and save them to the same directory.

[Abdallah alsuod]

I am using this code to get the results in here :

-------------------------------

For testing use a simple function: f = (x2 + 3x)2 over the interval of [0,1], with n = 2 and 3 levels of accuracy:

>> format long

>> f = inline('(x^2+3*x)^2');

>> I = Romberg(f,0,1,2,3)

I =

5.531250000000 4.700520833333 4.700000000000

4.908203125000 4.700032552083 0

4.752075195313 0 0

[Star Strider]

To quote from my previous Comment:

‘You need to go back to wherever you downloaded that file and download all the associated functions with it, and save them to the same directory.’

That will likely solve your problem.

Answer 1

[Uday Pradhan]

Hi,

As already mentioned in the comments, MATLAB cannot find the function "TrapComp", hence the error. Looking at the code, this function seems to be the composite Trapezoidal rule which itself is pretty simple to implement. You may use this as TrapComp:

function integral = TrapComp(f, a, b, n)
    h = (b-a)/n;
    result = 0.5*f(a) + 0.5*f(b);
    for q = 1:(n-1)
        result = result + f(a + q*h);
    end
    integral = h*result;
end

Results:

>> f = inline('(x^2+3*x)^2');
>> format long
>> I = Romberg(f,0,1,2,3)

I =

   5.531250000000000   4.700520833333333   4.700000000000000
   4.908203125000000   4.700032552083333                   0
   4.752075195312500                   0                   0

Hope this helps!

[Abdallah alsuod]

Thank you, that was the solution, I forgot about the function itself.