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  1. #include <iostream>
  2. #include <fstream>
  3. #include <cmath>
  4. #include <vector>
  5. #include <iomanip>
  6.  
  7. using namespace std;
  8.  
  9. // Constants for the Lorenz system
  10. const double sigma = 10.0;
  11. const double rho = 28.0;
  12. const double beta = 8.0 / 3.0;
  13.  
  14. // Lorenz equations
  15. vector<double> lorenz(double x, double y, double z) {
  16.     vector<double> dxdt(3);
  17.     dxdt[0] = sigma * (y - x);
  18.     dxdt[1] = x * (rho - z) - y;
  19.     dxdt[2] = x * y - beta * z;
  20.     return dxdt;
  21. }
  22.  
  23. // Euler method to solve the Lorenz system
  24. void euler_method(double x0, double y0, double z0, double dt, double t_max, const string& filename_prefix) {
  25.     double t = 0.0;
  26.     double x = x0, y = y0, z = z0;
  27.     int frame = 0;
  28.  
  29.     // Loop through time and output the state to files
  30.     while (t < t_max) {
  31.         stringstream filename;
  32.         filename << filename_prefix << setw(4) << setfill('0') << frame << ".dat"; // Generate frame filename
  33.         ofstream file(filename.str());
  34.  
  35.         file << x << " " << y << " " << z << endl;
  36.         file.close();
  37.  
  38.         // Compute the next state using the Lorenz equations
  39.         vector<double> dxdt = lorenz(x, y, z);
  40.         x += dxdt[0] * dt;
  41.         y += dxdt[1] * dt;
  42.         z += dxdt[2] * dt;
  43.  
  44.         t += dt;
  45.         frame++;
  46.     }
  47. }
  48.  
  49. int main() {
  50.     // Initial conditions
  51.     double x0 = 0.0, y0 = 1.0, z0 = 1.05;
  52.     double dt = 0.01;  // Time step
  53.     double t_max = 100.0;  // Total time
  54.  
  55.     // Run the simulation and generate data for animation
  56.     euler_method(x0, y0, z0, dt, t_max, "lorenz_frame_");
  57.  
  58.     return 0;
  59. }
  60.  
Success #stdin #stdout 0.07s 5280KB
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https://ideone.com/oODV0E
language:
C++14 (gcc 8.3)
created:
2 days ago
visibility:
public

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