ill_bvp


ill_bvp, a Python code which defines an ill conditioned boundary value problem (BVP), and calls on scipy.integrate.solve_bvp() to solve it with various values of the conditioning parameter.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

ill_bvp is available in a MATLAB version and a Python version.

Related Data and Programs:

bvp_fd, a Python code which demonstrates the use of the finite difference method (FDM) to solve a boundary value problem (BVP).

fd1d_bvp, a MATLAB code which applies the finite difference method (FDM) to a two point boundary value problem (BVP) in one spatial dimension.

fem1d_bvp_linear, a MATLAB code which applies the finite element method (FEM), with piecewise linear elements, to a two point boundary value problem (BVP) in one spatial dimension, and compares the computed and exact solutions with the L2 and seminorm errors.

fem1d_bvp_quadratic, a Python code which applies the finite element method (FEM), with piecewise quadratic (PWQ) elements, to a two point boundary value problem (BVP) in one spatial dimension.

solve_bvp_test, a Python code which calls scipy.integrate.solve_bvp(), which solves boundary value problems (BVP) in one spatial dimension.

Reference:

  1. Lloyd Trefethen,
    Eight perspectives on the exponentially ill-conditioned equation epsilon y" - xy' + y = 0,
    SIAM Review,
    Volume 62, Number 2, June 2020, pages 439-462.

Source code:


Last revised on 21 June 2022.