请帮我用C++写一个计算二重积分的程序
时间: 2023-08-21 11:07:33 浏览: 53
下面是一个简单的计算二重积分的程序,其中用到了 Simpson 积分法:
```c++
#include <iostream>
#include <cmath>
using namespace std;
double f(double x, double y) {
return x * x + y * y;
}
double simpson(double a, double b, double fa, double fb, double fab, double eps) {
double c = (a + b) / 2.0;
double fc = f(c, 0.5);
double sab = (b - a) * (fa + 4 * fc + fb) / 6.0;
double sac = (c - a) * (fa + 4 * f((a + c) / 2.0, 0.5) + fc) / 6.0;
double sbc = (b - c) * (fc + 4 * f((b + c) / 2.0, 0.5) + fb) / 6.0;
if (fabs(sab - sac - sbc) < eps) {
return sac + sbc;
} else {
return simpson(a, c, fa, fc, fab, eps / 2.0) + simpson(c, b, fc, fb, fab, eps / 2.0);
}
}
double integrate(double a, double b, double c, double d, double eps) {
double fa = f(a, 0.5);
double fb = f(b, 0.5);
double fab = (f(a, 0.5) + f(b, 0.5) + f(c, 0.5) + f(d, 0.5)) / 4.0;
return simpson(a, b, fa, fb, fab, eps) + simpson(c, d, f(c, 0.5), f(d, 0.5), fab, eps);
}
int main() {
double a = 0.0, b = 1.0, c = 0.0, d = 1.0;
double eps = 1e-6;
double res = integrate(a, b, c, d, eps);
cout << "The double integral of x^2 + y^2 over [0,1]x[0,1] is: " << res << endl;
return 0;
}
```
其中,`f` 函数是被积函数,`simpson` 函数是 Simpson 积分法的具体实现,`integrate` 函数是计算二重积分的函数,`main` 函数中给出了一个例子,即计算 $x^2 + y^2$ 在 $[0,1]\times[0,1]$ 上的二重积分。