fd1d_burgers_lax


fd1d_burgers_lax, a Fortran77 code which solves the nonviscous time-dependent Burgers equation using the finite difference method (FDM) and the Lax-Wendroff method.

The function u(x,t) is to be solved for in the equation:

du/dt + u * du/dx = 0
for 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.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

fd1d_burgers_lax is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version.

Related Data and Programs:

fd1d_burgers_lax_test

BURGERS, a dataset directory which contains some solutions to the viscous Burgers equation.

burgers_solution, a Fortran77 library which evaluates an exact solution of the time-dependent 1D viscous Burgers equation.

FD1D_ADVECTION_LAX, a Fortran77 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 Fortran77 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 Fortran77 program which applies the finite difference method to a two point boundary value problem in one spatial dimension.

FD1D_HEAT_EXPLICIT, a Fortran77 program which uses the finite difference method and explicit time stepping to solve the time dependent heat equation in 1D.

FD1D_HEAT_IMPLICIT, a Fortran77 program which uses the finite difference method and implicit time stepping to solve the time dependent heat equation in 1D.

FD1D_HEAT_STEADY, a Fortran77 program which uses the finite difference method to solve the steady (time independent) heat equation in 1D.

FD1D_PREDATOR_PREY, a Fortran77 program which implements a finite difference algorithm for predator-prey system with spatial variation in 1D.

FD1D_WAVE, a Fortran77 program which applies the finite difference method to solve the time-dependent wave equation utt = c * uxx in one spatial dimension.

Reference:

  1. Daniel Zwillinger,
    Handbook of Differential Equations,
    Academic Press, 1997,
    ISBN: 0127843965,
    LC: QA371.Z88.

Source Code:


Last revised on 07 December 2023.