DG1D_BURGERS a MATLAB library which uses the Discontinuous Galerkin Method (DG) to approximate a solution of the time dependent 1D Burgers Equation. The original version of the code was written by Jan Hesthaven and Tim Warburton.
A 1D version of the time dependent Burgers equation has the form
PDE:
du/dt + du^2/dx = 0 for -1 < x < +1
IC:
epsilon = 0.1
u(x,0) = - tanh ( ( x + 0.5 ) / ( 2 * epsilon ) ) + 1.0
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_BURGERS is available in a MATLAB version.
BVP4C, MATLAB programs which illustrate how to use the MATLAB command bvp4c(), which can solve boundary value problems (BVP's) in one spatial dimension.
DG1D_ADVECTION, a MATLAB library 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_HEAT, a MATLAB library 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 library 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 program which applies the discontinuous Galerkin method (DG) to a 1D version of the Poisson equation, by Beatrice Riviere.
FD1D_ADVECTION_DIFFUSION_STEADY, a MATLAB program 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 program 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 program 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 program 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 program 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 program which applies the finite difference method to a two point boundary value problem in one spatial dimension.
FD1D_HEAT_EXPLICIT, a MATLAB program which uses the finite difference method and explicit time stepping to solve the time dependent heat equation in 1D.
FD1D_HEAT_IMPLICIT, a MATLAB program which uses the finite difference method and implicit time stepping to solve the time dependent heat equation in 1D.
FD1D_HEAT_STEADY, a MATLAB program which uses the finite difference method to solve the steady (time independent) heat equation in 1D.
FD1D_PREDATOR_PREY, a MATLAB program which implements a finite difference algorithm for predator-prey system with spatial variation in 1D.
FD1D_WAVE, a MATLAB program which applies the finite difference method to solve the time-dependent wave equation in one spatial dimension.
FEM1D, a MATLAB program which applies the finite element method to a linear two point boundary value problem in a 1D region.
FEM1D_BVP_LINEAR, a MATLAB program 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.