Integration using Green's function in MatLab

I have an integration

phi(r)= int_0^{inf} (r'^2 * dr' * G(r,r') * S(r'))

where G(r,r') = 1/(2*m*r*r')*(exp(-m*(r-r')) - exp(-m*(r+r'))) and S(r') is a known dataset at each r' and m is also known.

How to deal with this integration to find phi(r). Could you please help me on this?

Answer 1

[Shubh Pareek]

Hi @pritha

From what i have understood you want to integrate phi function from 0 to infinity , may be this code can help

also since I didn't know what your dataset function S is so i specified it to be rprime itself.

m = 1; % Some constant value
r = 0.5; % Value of r to evaluate

% Define the function handles for G and S
G = @(r, rprime) 1./(2.*m.*r.*rprime).* (exp(-m.*(abs(r-rprime))) - exp(-m.*(r+rprime)));
S = @(rprime) rprime;% Define your dataset function here

% Define the integrand function
integrand = @(rprime) (rprime.^2) .* G(r, rprime) .* S(rprime);

% Evaluate the integral using MATLAB's integral function
phi_r = integral(integrand, 0, Inf)

phi_r = 2.0739

If you want to know more about integration with multiple variable or how integral function works here are some resources .

Integrating a multivariate function w.r.t. a single variable - MATLAB Answers - MATLAB Central (mathworks.com)

How I can integrate function if I have two variables? - MATLAB Answers - MATLAB Central (mathworks.com)

Numerical integration - MATLAB integral - MathWorks India

[Torsten]

I think a function of r for phi is more adequate here:

m = 1; % Some constant value
% Define the function handles for G and S
G = @(r, rprime) 1./(2.*m.*r.*rprime).* (exp(-m.*(abs(r-rprime))) - exp(-m.*(r+rprime)));
S = @(rprime) rprime;% Define your dataset function here
% Define the integrand function
integrand = @(r, rprime) (rprime.^2) .* G(r, rprime) .* S(rprime);
% Evaluate the integral using MATLAB's integral function
phi_r = @(r) integral(@(rprime)integrand(r, rprime), 0, Inf);
phi_r(0.5)

ans = 2.0739

[pritha]

Thanks for your reply @Shubh. I was not taking the abs(r-rprime). That's why I couldn't able to solve it. Thanks for helping me out. Thanks @Torsten for your reply. I am getting the result properly now.