艾里函数积分的根(matlab) [英] Roots of integral of Airy function (matlab)

问题描述

我想求解以下方程式

我在函数的定义上做错了一些，但还是不明白

I am doing something wrong with the definition of the function but I still don't get it

function F=myairyint(x)

F=integral(@(x)airy,x,1000)

end

functi2=@(x) myairyint;
x0=-1:-1:-15;
fsolve(functi2,x0)

为什么不起作用?

推荐答案

您的积分似乎在[-15 -1]中没有根，并且收敛到零.我已经通过绘图对其进行了测试:

Your integral seems to have no roots in [-15 -1] and converges to zero. I have tested it via plotting:

x0 = linspace(-20,20);
airyint = arrayfun(@(x0) integral(@(n) airy(n), x0, inf), x0);
plot(x0, airyint);

我还通过fzero()对其进行了测试，例如:

I also tested it via fzero() such as:

f = @(x) integral(@(n) airy(n), x, inf);
fzero(f, 0)

输出符合预期:

ans =

    115.8524

但是，似乎 x> 115.8524 的每个实数看起来都像是该积分方程的根.

But it seems like every real numbers for x > 115.8524 will look like roots of this integral equation.

其他:

fzero()是一个试图寻找根的函数，该根着眼于两个动态间隔之间的函数值.如果它捕获负值和正值，则它缩小了捕获根的间隔.但是存在错误率，因为您也可以从此示例中观察到.仅当x变为无穷大时，该方程才为零，这意味着该方程没有实际根.

fzero() is a function trying to find roots looking at the values of funtion between two dynamic intervals. If it catches minus and positive values, it is narrowing the interval to catch the root. But there is an error rate since you also can observe from this example. This equation will be zero only when x goes to infinity which means there is no real roots of this equation.

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