FD1D_BURGERS_LAX
Finite Difference Non-viscous Burgers Equation
Lax-Wendroff Method

FD1D_BURGERS_LAX is a FORTRAN90 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 = 0

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 GNU LGPL license.

Languages:

FD1D_BURGERS_LAX is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

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

BURGERS_SOLUTION, a FORTRAN90 library which evaluates an exact solution of the time-dependent 1D viscous Burgers equation.

FD1D_ADVECTION_LAX, a FORTRAN90 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 FORTRAN90 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 FORTRAN90 program which applies the finite difference method to a two point boundary value problem in one spatial dimension.

FD1D_HEAT_EXPLICIT, a FORTRAN90 program which uses the finite difference method and explicit time stepping to solve the time dependent heat equation in 1D.

FD1D_HEAT_IMPLICIT, a FORTRAN90 program which uses the finite difference method and implicit time stepping to solve the time dependent heat equation in 1D.

FD1D_HEAT_STEADY, a FORTRAN90 program which uses the finite difference method to solve the steady (time independent) heat equation in 1D.

FD1D_PREDATOR_PREY, a FORTRAN90 program which implements a finite difference algorithm for predator-prey system with spatial variation in 1D.

FD1D_WAVE, a FORTRAN90 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:

• fd1d_burgers_lax.f90, the source code.

Examples and Tests:

• fd1d_burgers_lax.txt, the output file.

List of Routines:

• MAIN is the main program for FD1D_BURGERS_LAX.
• R8VEC_EVEN returns an R8VEC of evenly spaced values.
• REPORT prints or plots or saves the data at the current time step.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• U_A sets the boundary condition for U at A.
• U_B sets the boundary condition for U at B.
• U_INIT sets the initial condition for U.

You can go up one level to the FORTRAN90 source codes.