C++ 程序已停止工作 - 求解常微分方程

Question

我正在编写一个 C++ 程序来为大学作业寻找一阶微分方程的解。程序启动，然后一旦我输入要执行的迭代次数，我就会收到错误消息“Euler 的 method.exe 已停止工作”。这是我的代码:

#include <functional>
#include <vector>

using namespace std;

 
double f_r(double x, double r) {  
  return r;
  } 

double f_s(double x, double s) {
  return -x/s;  
  }
 

double eulerstep(const function<double(double,double)>& f, double xsub0, double ysub0, double h) {
  double ysub1 = ysub0+ h * f(xsub0,ysub0);
  return ysub1;
  }


double euler(const function<double(double,double)>& f, double xsub0, double ysub0, double h, int n) {
  vector<double> xsub;
  vector<double> ysub;
  xsub[0] = xsub0;
  ysub[0] = ysub0;
  n = ysub.size();
  for (int i=1; i<n; i++){
  	xsub[i+1] = xsub[i] + h;
  	ysub[i+1] = ysub[i] + h * f(xsub[i],ysub[i]);
  	cout << xsub[i] << " , " << ysub[i] << endl;
  }
  return ysub[n];
  }
  
int main() {
  int nsteps = 0;
  cout << "Number of steps?" << endl;
  cin >> nsteps;
  double h = 1.0 / nsteps;

  double r = euler(f_r,0,1,h,nsteps);
  

  double s = euler(f_s,0,1,h,nsteps);
 
  return 0;
}

我相当确定问题在于我如何定义我的 vector ，但我是使用它们的新手，所以看不出我哪里出错了。如果有人能指出我方法中的错误，我将不胜感激

谢谢

Answer 1

这是一个更新的函数。您必须设置大小，而不是向空 vector 询问其大小。

double euler(const function<double(double, double)>& f, double xsub0, double ysub0, double h, int n)
{
    vector<double> xsub;
    vector<double> ysub;
    xsub.resize(n+1); // so we can access [n], it must be size n+1
    ysub.resize(n+1);
    xsub[0] = xsub0;
    ysub[0] = ysub0;
    for (int i = 1; i<n; i++) {
        xsub[i + 1] = xsub[i] + h;
        ysub[i + 1] = ysub[i] + h * f(xsub[i], ysub[i]);
        cout << xsub[i] << " , " << ysub[i] << endl;
    }
    return ysub[n];
}