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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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 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* ;

Jarrod Rivituso
on 20 May 2011

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)

Note that here we are using meshgrid to calculate a range of x1,x2 values over a grid, and then for each x1 and x2 we are repeating the quad call

Hope this helps!

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