Integration using Green's function in MatLab

Question

pritha 2023-6-11

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1981524-integration-using-green-s-function-in-matlab

评论： pritha 2023-6-12

采纳的回答： Shubh Pareek

int.png

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?

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Shubh Pareek 2023-6-12

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1981524-integration-using-green-s-function-in-matlab#answer_1254069

在 MATLAB Online 中打开

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

2 个评论
显示无隐藏无

Torsten 2023-6-12

在 MATLAB Online 中打开

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 2023-6-12

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.

请先登录，再进行评论。