How to calculate double integral?

Question

Hexe 2022-12-16

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1879852-how-to-calculate-double-integral

评论： Hexe 2022-12-16

Hi! I have a problem with solution of double integral. The syms solves too long and it cannot be used.But in another way I have problem.

I have an integral fun2 on z and it has x which is a variable in the integral fun0. How can I set a variable x to first calculate the integral f2 over z, and then integral f3 over x? (Of course, when I set x=some number I obtain a curve or a set of curves if x=0:0.1:1 and make for j = 1:length(x), but I doubt about this result, because the behavior of curves is not correct).

clear all, close all

n=1;

t=1;

r=1;

s=0:0.2:10;

for i = 1:length(s)

k=s(i);

fun2=@(z)(z.*exp(2.*n.*t.*z.^2).*(besselj(0,(k.*z.*x)))./sqrt(1-z.^2));

f2(i,:)=integral(fun2,0,1);

fun0=@(x)(((((x.^2.*exp(-2.*t.*x.^2)./(x.^2+1/(r.^2)).^2)))).*f2(i));

f3(i,:)=integral(fun0,0,inf);

end

Cor=8/(r*(pi)^(3/2))*sqrt(2*n*t)*exp(-2*n*t)/(erf(sqrt(2*n*t))*((1+4*t/r^2)*exp(2*t/r^2)*erfc(sqrt(2*t/r^2))-2*sqrt(2*t)/(r*sqrt(pi)))).*f3;

plot(s,Cor,'b-');

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Answer 1

Torsten 2022-12-16

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1879852-how-to-calculate-double-integral#answer_1129672

编辑：Torsten 2022-12-16

在 MATLAB Online 中打开

n = 1 ;

t = 1;

r = 1;

s = 0:0.2:10;

fun = @(x,z,k) x.^2.*exp(-2.*t.*x.^2)./(x.^2+1/r^2).^2 .* z.*exp(2*n*t.*z.^2).*besselj(0,k.*z.*x)./sqrt(1-z.^2);

f3 = arrayfun(@(k)integral2(@(x,z)fun(x,z,k),0,Inf,0,1),s)

f3 = 1×51

0.2959 0.2948 0.2915 0.2860 0.2784 0.2690 0.2579 0.2454 0.2316 0.2169 0.2015 0.1857 0.1697 0.1538 0.1381 0.1229 0.1083 0.0945 0.0815 0.0694 0.0583 0.0483 0.0392 0.0311 0.0240 0.0177 0.0123 0.0077 0.0038 0.0005

Cor = 8/(r*(pi)^(3/2))*sqrt(2*n*t)*exp(-2*n*t)/(erf(sqrt(2*n*t))*((1+4*t/r^2)*exp(2*t/r^2)*erfc(sqrt(2*t/r^2))-2*sqrt(2*t)/(r*sqrt(pi))))*f3

Cor = 1×51

1.0000 0.9962 0.9849 0.9663 0.9409 0.9091 0.8716 0.8292 0.7828 0.7331 0.6811 0.6276 0.5735 0.5196 0.4667 0.4153 0.3659 0.3192 0.2753 0.2346 0.1972 0.1631 0.1324 0.1051 0.0809 0.0598 0.0416 0.0259 0.0127 0.0017

plot(s,Cor,'b-')

grid on