bvp_shooting, a Python code which uses the shooting method to solve a second order two-point boundary value problem (BVP) with left and right Dirichlet boundary conditions.
The strategy is to use an ODE solver, for which we use the given left Dirichlet boundary condition y(a) = ya, and an artificial Neumann boundary condition y'(a) = alpha. We solve the ODE, and compare the computed value y(b) to the desired value yb. The difference is a residual which we wish to drive to zero. We do this by employing a secant method approach.
The information on this web page is distributed under the MIT license.
bvp_shooting is available in a MATLAB version and an Octave version and a Python version.
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 Python code which applies the finite difference method (FDM) to a two point boundary value problem (BVP) in one spatial dimension.
fem1d, a Python code which applies the finite element method (FEM) to a 1D linear two point boundary value problem (BVP).
fem1d_bvp_linear, a Python 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 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.
