Wed Sep 11 08:42:42 2024

convergence_test():
  python version: 3.10.12
  numpy version:  1.26.4
  Test convergence().

convergence_n_test01():
  A computation has been carried out with n=2^k intervals,
  where n = 8, 16, ..., 512, and for each n, the
  approximation error e(n) was computed.
  convergence_n() estimates the convergence order.

  The number of computations was  7
  The size n = 2^k was
[  8  16  32  64 128 256 512]
  The errors e(n):
[1.17e-02 1.76e-04 9.94e-05 2.40e-06 2.02e-07 6.46e-09 3.07e-10]

    n(k)  error(k)   eoc(k)

    8  1.17e-02  nan
   16  1.76e-04  6.05
   32  9.94e-05  0.82
   64  2.40e-06  5.37
  128  2.02e-07  3.57
  256  6.46e-09  4.97
  512  3.07e-10  4.40

  eoc mean       4.20

convergence_n_test02():
  A computation has been carried out with n=2^k intervals,
  where n = 8, 16, ..., 512, and for each n, the
  approximation error e(n) was computed.
  convergence_n() estimates the convergence order.

  The number of computations was  6
  The size n = 2^k was
[  4   8  16  32  64 128]
  The errors e(n):
[6.05759e-05 2.04755e-05 5.66053e-06 1.47327e-06 3.74947e-07 9.45143e-08]

    n(k)  error(k)   eoc(k)

    4  6.06e-05  nan
    8  2.05e-05  1.56
   16  5.66e-06  1.85
   32  1.47e-06  1.94
   64  3.75e-07  1.97
  128  9.45e-08  1.99

  eoc mean       1.86

convergence_h_test01():
  A computation has been carried out with intervals,
  of size h(k), for k = 1 to 5.  For each h, the
  approximation error e(k) was computed.
  convergence_h() estimates the convergence order.

  The number of computations was  5
  The mesh sizes h(k):
[0.25     0.125    0.0625   0.03125  0.015625]
  The errors e(k):
[0.069288   0.0185749  0.00479553 0.00121795 0.00030689]

    h(k)  error(k)   eoc(k)

  0.250000  6.93e-02  nan
  0.125000  1.86e-02  1.90
  0.062500  4.80e-03  1.95
  0.031250  1.22e-03  1.98
  0.015625  3.07e-04  1.99

  eoc mean            1.95

convergence_test():
  Normal end of execution.
Wed Sep 11 08:42:42 2024