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

FD1D_BURGERS_LAX, a MATLAB 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
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.

### Usage:

fd1d_burgers_lax
runs the program.

### 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_CHARACTERISTICS, a MATHEMATICA program which solves the time dependent inviscid Burgers equation using the method of characteristics, by Mikel Landajuela.

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

BURGERS_STEADY_VISCOUS, a MATLAB library which solves the steady (time-independent) viscous Burgers equation using a finite difference discretization of the conservative form of the equation, and then applying Newton's method to solve the resulting nonlinear system.

BURGERS_TIME_VISCOUS, a MATLAB library which solves the time-dependent viscous Burgers equation using a finite difference discretization of the conservative form of the equation.

FD1D_ADVECTION_LAX, 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 method to treat the time derivative.

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.

PCE_BURGERS, a MATLAB program which defines and solves a version of the time-dependent viscous Burgers equation, with uncertain viscosity, using a polynomial chaos expansion in terms of Hermite polynomials, by Gianluca Iaccarino.

### Reference:

1. Daniel Zwillinger,
Handbook of Differential Equations,