Need to apply trapezoidal rule for double integration with an array by using the for loop

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GAYTRI ARYA 2021-6-22

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评论： GAYTRI ARYA 2021-6-24

z=(0:0.1:10);

F1= @(r1,r2)exp(-(r1.^2+r2.^2).*A).*exp(-i*B.*z.*(r1.^2+r2.^2)).*besseli(n,r1.*r2./(sig^2)).*r1.*r2;

I want to use trapezoidal numerical integration on the F1 for the variables r1 and r2 for which limits are 0 to 1, where z is a matrix. The direct command of integral2 cannot be applied due to the array function. I am stuck at first loop, where the error "Conversion to double from function handle is not possible" is showing. Please help. Thanks in advance.

for i=1:m

xi=i*h;

sumx(i)=@(r2)F1(xi);

i=i+1;

end

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Sargondjani 2021-6-23

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There are two things that need correction:

1) Remove the line i=i+1. This is what the for loop does. (also don't use "i" in general because i=sqrt(-1)))

2) The funciton handle. I will try to explain how function handles work. I have a function:

F = @(a,b,X1,X2)a*X1.^2 + b*X2.^2;

a,b are parameters. I will set them, for example a=1, b=2;

Now i want to loop over X1, given values of a, b, and X2:

a=1;
b=2;
X2 = 0.1;
h=0.001;
y = NaN(1,m);
for ii = 1:m
    X1 = ii*h;
    y(1,ii) = F(a,b,X1,X2);
end

Now the value of F, given a,b,X1(ii),X2 are assigned to y(ii). I hope that clarifies something.

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Sargondjani 2021-6-23

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You NEED to specify the value of BOTH r1 and r2, when you want to evaluate F1. Otherwise, how should matlab know hwo to calculate the value of F1

Anyway, what i think you want to do is:

%loop over value of r1:
for ii = 1:m
 r1 = ii*h
% take 1d integral for r2 (given value of r1)
f_int_r2 = @(r2)F1(r1,r2);
q(1,ii) = integral(f_int_r2,0,1);
end

Anyway, I am pretty sure you can do this with the function integral2. Just it's not clear how z comes into play... is it a 3rd variable? Or you want to know the double integral for each value of z? Then you should loop over z...

GAYTRI ARYA 2021-6-24