DG1D_HEAT is 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.
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
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DG1D_HEAT 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_BURGERS, a MATLAB library 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, 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.