FD1D_BURGERS_LAX, a C++ program which solves the nonviscous time-dependent Burgers equation using finite differences and the Lax-Wendroff method.
The function u(x,t) is to be solved for in the equation:
du/dt + u * du/dx = 0for a <= x <= b and t_init <= t <= t_last.
Problem data includes an initial condition for u(x,t_init), and the boundary value functions u(a,t) and u(b,t).
The non-viscous Burgers equation can develop shock waves or discontinuities.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
FD1D_BURGERS_LAX is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.
BURGERS, a dataset directory which contains some solutions to the viscous Burgers equation.
BURGERS_SOLUTION, a C++ library which evaluates an exact solution of the time-dependent 1D viscous Burgers equation.
FD1D_ADVECTION_LAX, a C++ 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 method to treat the time derivative.
FD1D_BURGERS_LEAP, a C++ 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 C++ program which applies the finite difference method to a two point boundary value problem in one spatial dimension.
FD1D_HEAT_EXPLICIT, a C++ program which uses the finite difference method and explicit time stepping to solve the time dependent heat equation in 1D.
FD1D_HEAT_IMPLICIT, a C++ program which uses the finite difference method and implicit time stepping to solve the time dependent heat equation in 1D.
FD1D_HEAT_STEADY, a C++ program which uses the finite difference method to solve the steady (time independent) heat equation in 1D.
FD1D_WAVE, a C++ program which applies the finite difference method to solve the time-dependent wave equation utt = c * uxx in one spatial dimension.