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квадратур метод

Dec 20th, 2016
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  1. static void DifferenceMethod()
  2. {
  3. double begin = 0;
  4. double end = 12;
  5. double[] x = new double[N];
  6. double[] y = new double[N];
  7. double[] yt = new double[N];
  8. double[] e = new double[N];
  9. double[] p = new double[N + 1];
  10. double[] q = new double[N + 1];
  11. double h = end - begin;
  12. h /= N;
  13. x[0] = begin;
  14.  
  15. for (int i = 1; i < N; i++)
  16. x[i] = x[i - 1] + h;
  17.  
  18. for (int i = 0; i < N; i++)
  19. {
  20. double a, b, c, d;
  21.  
  22. d = (Math.Pow(x[i], 6) - 12 * Math.Pow(x[i], 5) + 3 * Math.Pow(x[i], 4) - 2 * 12 * Math.Pow(x[i], 3) + 6 * x[i] - 2 * 12) *( h * h) / 2;
  23. a = 1 / 2 - x[i] * x[i] / 4 * h;
  24. b = 1 / 2 + h * x[i] * x[i] / 4;
  25. c = -(-1 + x[i] * x[i] * x[i] / 2 * h);
  26.  
  27. if (i == N - 1) p[i + 1] = 0;
  28. else p[i + 1] = b / (c - a * p[i]);
  29.  
  30. q[i + 1] = (d + a * q[i]) / (c - a * p[i]);
  31. }
  32.  
  33. for (int i = N - 2; i > 0; i--)
  34. y[i] = p[i + 1] * y[i+1] + q[i + 1];
  35.  
  36. for (int i = 1; i < N - 1; i++)
  37. {
  38. yt[i] = Math.Pow(x[i], 3) - 12 * Math.Pow(x[i], 2);
  39. e[i] = Math.Abs(yt[i]- y[i]);
  40. }
  41.  
  42.  
  43. Console.WriteLine("Шаг: ");
  44. foreach(double i in x)
  45. Console.Write("{0:F5} | ", i);
  46.  
  47. Console.WriteLine("\n \n Y:");
  48. foreach(double i in y)
  49. Console.Write("{0:F5} | ", i);
  50.  
  51. Console.WriteLine("\n \n Y точные:");
  52. foreach(double i in yt)
  53. Console.Write("{0:F5} | ", i);
  54.  
  55. Console.WriteLine(" \n \n точность");
  56. foreach(double i in e)
  57. Console.Write("{0:F5} | ", i);
  58. }
  59.  
  60. static void Main(string[] args)
  61. {
  62. DifferenceMethod();
  63. }
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