dg1d_advection, a MATLAB code which uses the Discontinuous Galerkin Method (DG) to approximate a solution of the unsteady 1D advection equation. The original version of the code was written by Jan Hesthaven and Tim Warburton.
A 1D version of the advection equation has the form
du/dt + 2 pi du/dx = 0 for 0 < x < 2 u(0,t) = - sin(2*pi*t) u(x,0) = sin(x)
Permission to use this software for noncommercial research and educational purposes is hereby granted without fee. Redistribution, sale, or incorporation of this software into a commercial product is prohibited. THE AUTHORS OR PUBLISHER DISCLAIMS ANY AND ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR ANY PARTICULAR PURPOSE. IN NO EVENT SHALL THE AUTHORS OR THE PUBLISHER BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS.
dg1d_advection is available in a MATLAB version.
bvp4c_test, a MATLAB code which uses the MATLAB command bvp4c(), which can solve boundary value problems (BVP's) in one spatial dimension.
dg1d_burgers, a MATLAB code which uses the Discontinuous Galerkin Method (DG) to approximate a solution of the unsteady 1D Burgers Equation. The original version of the code was written by Jan Hesthaven and Tim Warburton.
dg1d_heat, a MATLAB code which uses the Discontinuous Galerkin Method (DG) to approximate a solution of the unsteady 1D heat Equation. The original version of the code was written by Jan Hesthaven and Tim Warburton.
dg1d_maxwell, a MATLAB code which uses the Discontinuous Galerkin Method (DG) to approximate a solution of Maxwell's equations. The original version of the code was written by Jan Hesthaven and Tim Warburton.
dg1d_poisson, a MATLAB code which applies the discontinuous Galerkin method (DG) to a 1D version of the Poisson equation, by Beatrice Riviere.
fd1d_advection_diffusion_steady, a MATLAB code which applies the finite difference method to solve the steady advection diffusion equation v*ux-k*uxx=0 in one spatial dimension, with constant velocity v and diffusivity k.
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_advection_lax_wendroff, 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 Lax-Wendroff method to treat the time derivative.
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 a two point boundary value problem in one spatial dimension.
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.
The original MATLAB source code was written by Jan Hesthaven and Tim Warburton.