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.
The computer code and data files made available on this web page are distributed under the MIT license
ill_bvp is available in a MATLAB version.
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.