Integration symbiolic form in matlab gives error

%here is my matlab script

Part_1=@(r,theta) 1+(2.*(1+r.*cos(theta))).^2;

W_i=@(r,theta) Part_1(r,theta).*(whittakerW(50, 0.5,(2.*(r))./(50)));

Matrix_element=(quad2d(W_i,0.5, 2000,0,pi));

This gives me error. What is the best way to solve this integration?

Answer 1

[Jaimin]

Hi @Anal

The error in your MATLAB script likely arises from the way you are using the “whittakerW” function and the “quad2d” function.

Ensure that the function handles you are using are properly vectorized. The “quad2d” function expects the integrand to accept arrays as inputs and return an array of outputs.

Make sure that the “whittakerW” function is available in your MATLAB environment. This function is part of the Symbolic Math Toolbox, so ensure you have it installed and the toolbox is loaded.

Kindly refer to the following code snippet for understanding.

% Define the function Part_1
Part_1 = @(r, theta) 1 + (2 .* (1 + r .* cos(theta))).^2;

% Define the function W_i, ensuring vectorization
W_i = @(r, theta) Part_1(r, theta) .* whittakerW(50, 0.5, (2 .* r) ./ 50);

% Perform the double integration using quad2d
Matrix_element = quad2d(W_i, 0.5, 2000, 0, pi);

% Display the result
disp(Matrix_element);

Kindly refer following MathWorks documentation for more information:

quad2d: https://www.mathworks.com/help/matlab/ref/quad2d.html

whittakerW: https://www.mathworks.com/help/symbolic/sym.whittakerw.html

I hope this will be helpful.

[Anal]

Hi, “whittakerW” function is availble in my Symbiolic math toolbox. I have previously used that. Still it is not working.

Answer 2

[Torsten]

I think you will have big problems if you try to integrate a function with values in the order of +/- 1e70.

syms r theta
Part_1= 1+(2*(1+r*cos(theta)))^2;
W_i = Part_1*whittakerW(50,0.5,2*r/50);
M = int(W_i,theta,0,pi);
rad = 0.5:0.5:2000;
plot(rad,double(subs(M,r,rad)))    

Answer 3

[Star Strider]

If you have R2012a or later, use the integral2 function instead —

Part_1=@(r,theta) 1+(2.*(1+r.*cos(theta))).^2;
W_i=@(r,theta) Part_1(r,theta).*(whittakerW(50, 0.5,(2.*(r))./(50)));
Matrix_element=(integral2(W_i,0.5, 2000,0,pi))

Matrix_element = -2.7744e+72

clearvars

syms r theta
Part_1(r,theta) = 1+(2*(1+r*cos(theta)))^2;
W_i(r,theta) = Part_1(r,theta).*(whittakerW(50, 0.5,(2*(r))/(50)));
Matrix_element=int(int(W_i,r,0.5, 2000), theta,0,pi)
Matrix_element = vpa(Matrix_element)

The symbolic results do not show up here after submitting the post.

.

[Anal]

thanks it was helpful