ill_bvp


ill_bvp, a MATLAB code which defines an ill conditioned boundary value problem, and calls on bvp4c() to solve it with various values of the conditioning parameter.

Licensing:

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

Languages:

ill_bvp is available in a MATLAB version.

Related Data and Programs:

ill_bvp_test

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

bvp_shooting_test, a MATLAB code which demonstrates the use of the shooting method to solve a boundary value problem (BVP).

bvp4c_test, a MATLAB code which calls bvp4c(), which can solve boundary value problems (BVP) in one spatial dimension.

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, a MATLAB code which applies the finite element method (FEM) to a 1D linear two point boundary value problem (BVP).

fem1d_adaptive, a MATLAB code which applies the finite element method (FEM) to a 1D linear two point boundary value problem (BVP) using adaptive refinement to improve the solution.

fem1d_bvp_linear, a MATLAB code which applies the finite element method (FEM), with piecewise linear (PWL) 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 MATLAB 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, and compares the computed and exact solutions with the L2 and seminorm errors.

fem1d_lagrange, a MATLAB code which sets up the matrices and vectors associated with the finite element method (FEM) solution of a boundary value problem (BVP) -u''+u=f(x), using Lagrange basis polynomials.

fem1d_nonlinear, a MATLAB code which applies the finite element method (FEM) to a 1D nonlinear two point boundary value problem (BVP).

fem1d_pmethod, a MATLAB code which applies the p-method version of the finite element method (FEM) to a 1D linear two point boundary value problem (BVP).

fem1d_spectral_numeric, a MATLAB code which applies the spectral finite element method (FEM) to solve the two point boundary value problem (BVP) u'' = - pi^2 sin(x) over [-1,+1] with zero boundary conditions, using as basis elements the functions x^n*(x-1)*(x+1), and carrying out the integration numerically, using the MATLAB quad() function, by Miro Stoyanov.

fem1d_spectral_symbolic, a MATLAB code which applies the spectral finite element method (FEM) to solve the two point boundary value problem (BVP) u'' = - pi^2 sin(x) over [-1,+1] with zero boundary conditions, using as basis elements the functions x^n*(x-1)*(x+1), and carrying out the integration using the MATLAB symbolic toolbox, by Miro Stoyanov.

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 modified on 21 June 2022.