dg1d_heat, an Octave 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.
A 1D version of the time dependent heat equation has the form
du/dt = d2u/dx2 for 0 < x < 2*pi
u(0,t) = 0 Boundary conditions
u(2*pi,t) = 0
u(x,0) = sin(x) Initial condition
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_heat is available in a MATLAB version and an Octave version.
bvp4c_test, an Octave code which illustrates how to use the bvp4c() function, which solves boundary value problems (bvp) in one spatial dimension.
dg1d_advection, an Octave code which uses the discontinuous Galerkin method (DG) to approximate a solution of the advection equation. The original version of the code was written by Jan Hesthaven and Tim Warburton.
dg1d_burgers, an Octave 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_maxwell, an Octave 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, an Octave code which applies the discontinuous Galerkin method (DG) to a 1d version of the Poisson equation, by Beatrice Riviere.
fd1d_advection_diffusion_steady, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which applies the finite difference method to a two point boundary value problem in one spatial dimension.
fd1d_heat_explicit, an Octave code which uses the finite difference method and explicit time stepping to solve the time dependent heat equation in 1d.
fd1d_heat_implicit, an Octave code which uses the finite difference method and implicit time stepping to solve the time dependent heat equation in 1d.
fd1d_heat_steady, an Octave code which uses the finite difference method to solve the steady (time independent) heat equation in 1d.
fd1d_predator_prey, an Octave code which implements a finite difference algorithm for predator-prey system with spatial variation in 1d.
fd1d_wave, an Octave code which applies the finite difference method to solve the time-dependent wave equation in one spatial dimension.
fem1d, an Octave code which applies the finite element method to a linear two point boundary value problem in a 1d region.
fem1d_bvp_linear, an Octave code which applies the finite element method, with piecewise linear elements, to a two point boundary value problem in one spatial dimension.
Jan Hesthaven, Tim Warburton. Modifications by John Burkardt.