biharmonic_cheby1d, a MATLAB code which uses Chebyshev methods to solve the biharmonic equation over an interval, a fourth order two point boundary value problem (BVP) in one spatial dimension.
The boundary value problem has the form:
d^4/dx^4 u(x) = exp(x)in the interval [-1,+1], with boundary conditions
u (-1) = 0 u (+1) = 0 u'(-1) = 0 u'(+1) = 0
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
biharmonic_cheby1d is available in a MATLAB version.
biharmonic_2d, a MATLAB code which deals with the biharmonic equation in two dimensions, whose simplest form is uxxxx + 2uxxyy + uyyyy = f.
biharmonic_fd1d, a MATLAB code which applies the finite difference method to solve the biharmonic equation over an interval, a fourth order two point boundary value problem (BVP) in one spatial dimension.
bvp4c_test, a MATLAB code which uses the MATLAB command bvp4c(), which can solve boundary value problems (bvp's) in one spatial dimension.
fd1d_advection_ftcs, a MATLAB code which applies the finite difference method to solve the time-dependent advection equation ut = - c * ux in one spatial dimension, with a constant velocity, using the ftcs method, forward time difference, centered space difference.
fd1d_burgers_lax, a MATLAB code which applies the finite difference method and the lax-wendroff method to solve the non-viscous time-dependent burgers equation in one spatial dimension.
fd1d_burgers_leap, a MATLAB code which applies the finite difference method and the leapfrog approach to solve the non-viscous time-dependent burgers equation in one spatial dimension.
fd1d_bvp, a MATLAB code which applies the finite difference method to solve a two point boundary value problem (BVP) in one spatial dimension.
fd1d_display, a MATLAB code which reads a pair of files defining a 1d finite difference model, and plots the data.
fd1d_heat_explicit, a MATLAB code which uses the finite difference method and explicit time stepping to solve the time dependent heat equation in 1d.
fd1d_heat_implicit, a MATLAB code which uses the finite difference method and implicit time stepping to solve the time dependent heat equation in 1d.
fd1d_heat_steady, a MATLAB code which uses the finite difference method to solve the steady (time independent) heat equation in 1d.
fd1d_predator_prey, a MATLAB code which implements a finite difference algorithm for predator-prey system with spatial variation in 1d.
fd1d_wave, a MATLAB code which applies the finite difference method to solve the time-dependent wave equation in one spatial dimension.
fem1d, a MATLAB code which applies the finite element method to a linear two point boundary value problem in a 1d region.
fem1d_bvp_linear, a MATLAB code which applies the finite element method, with piecewise linear elements, to a two point boundary value problem in one spatial dimension.