Evaluating a complex integral

Question

Michael Devereux 2019-2-14

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/445002-evaluating-a-complex-integral

回答： Abhishek Hullur 2021-8-8

采纳的回答： Torsten

在 MATLAB Online 中打开

Hello I'm trying to integrate the following function in MATLAB

but it's returing the wrong answer when I try something like

This is what I have tried so far:

fun = @(t,x,y) exp(1i.*(t.^4+x.*t.^2+y.*t));
P = @(x,y) integral(@(t)fun(t,x,y),-Inf,Inf);
P(1,1)

Any help appreciated and many thanks in advance

3 个评论
显示 1更早的评论隐藏 1更早的评论

Torsten 2019-2-15

exp(i*(t^4+x*t^2+y*t)) does not tend to 0 as | t| -> Inf. Thus your integral does not exist (at least in the usual sense).

Michael Devereux 2019-2-15

According to WolframAlpha the answer is 1.20759 + 0.601534 i

Keep in mind it's a complex exponential so there is a finite solution. This is know as the Pearcey Integral. I am more concerned that I have entered the formula incorrectly than the actual integral itself. Is this the correct way to approach the problem.

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Torsten 2019-2-15

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/445002-evaluating-a-complex-integral#answer_361192

format long
fun = @(t,x,y) exp(-t.^4 + 1i.*y.*t - x.*t.^2 + 1i*pi*0.125);    
P = @(x,y) integral(@(t)fun(t,x*exp(-1i*pi*0.25),y*exp(1i*pi*0.125)),-Inf,Inf); 
P(1,1)

Reference:

https://arxiv.org/pdf/1601.03615.pdf