how do I write the intergration part of an equation into matlab

Question

ken 2011-5-19

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/7795-how-do-i-write-the-intergration-part-of-an-equation-into-matlab

Hello everyone!

I'm trying to write out an equation from a book so that I can make a graph. I am stuck on how to write the intergration part of the equation.

I have uploaded a picture of the page here: http://www.flickr.com/photos/61865210@N07/5736930748/

I am trying to write equation 4.19

The code I have wriiten so far is below. Do I have to use ode45? I've looked in the help file but I don't understand it >.<

Thank you for your help!

ken

clear all
clc
[x,y] = meshgrid(-1:.5:1); 
%x=x+5;
L=0.5;
constant=-1/(4*pi);
ln1=log(x^2+(y-l)^2);
= ode(ln1)
ans=constant* ;

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ken 2011-5-20

Can anyone help me please? I've been looking for examples online but can't find any which solve equations similar to mine.

Inputting the x1 and x2 is confusing me.

Thanks!

ken

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Answer 1

Jarrod Rivituso 2011-5-20

2
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/7795-how-do-i-write-the-intergration-part-of-an-equation-into-matlab#answer_10814

在 MATLAB Online 中打开

I would start by simplifying the problem a bit.

Step 1 - for a fixed x1,x2, how could I calculate the integral?

For this, you can actually use the quad function (you don't need ode45). Let's assume x1 = 7 and x2 = 3. I could create a function that would return the value of the integrand for any particular L

integrand = @(L) log(7.^2+(3-L).^2);
integrand(14)

I can then use this function to do the integral numerically

quad(integrand,-5,5)

So, we've solve step 1! :)

Step 2 - Repeat process for a bunch of x1,x2 combos

Well, this is fairly straightforward now that we solved step 1. We just use a loop.

lambda = 1;
x1 = 1:0.1:2;
x2 = 1:0.1:2;
[X1,X2] = meshgrid(x1,x2);
phi = zeros(size(X1));
for i = 1:numel(X1)
    fixedx1x2 = @(L) log(X1(i).^2+(X2(i)-L).^2);
    phi(i) = (lambda / 4*pi) * quad(fixedx1x2,-5,5);
end
surf(X1,X2,phi)