Richardson外推法計算給定點處的一階和二階導數

//計算給定點處的一階和二階導數
#include <iostream>
#include <math.h>

using namespace std;

class deriv
{
private:
 int k;
 double d1, d1_1, d1_2, d2, d2_1, d2_2, d1_new, d2_new;
 double f_x, f_xhm, f_x2hm, f_xhp, f_x2hp, h, x;

public:
 double func(double y)
 {
  double f = 1 / sqrt(y) - 1.77 * log(1e4 * sqrt(y)) + 0.5;
  return f;
 }
 void diffn();
};

void main()
{
 deriv differentiate;
 differentiate.diffn();
}

void deriv::diffn()
{
 cout << "\n輸入要計算導數的點：";
 cin >> x;
 cout << "\n輸入步長h：";
 cin >> h;
 for (k = 0; k <= 1; k++)
 {
  f_x = func(x);
  f_xhp = func(x + h);
  f_x2hp = func(x + 2 * h);
  f_xhm = func(x - h);
  f_x2hm = func(x - 2 * h);
  d1 = (-f_x2hp + 8 * f_xhp - 8 * f_xhm + f_x2hm) / (12 * h);
  d2 = (-f_x2hp + 16 * f_xhp - 30 * f_x + 16 * f_xhm - f_x2hm) / (12 * h * h);
  if (k == 0)
  {
   d1_1 = d1;
   d2_1 = d2;
  }
  if (k == 1)
  {
   d1_2 = d1;
   d2_2 = d2;
  }
  h /= 2.0;
 }
 d1_new = (16 * d1_2 - d1_1) / 15;
 d2_new = (16 * d2_2 - d2_1) / 15;
 cout << "\n在" << x << "點的一階導數 = " << d1_new << endl;
 cout << "\n在" << x << "點的二階導數 = " << d2_new << endl;
}