# fd1d_burgers_leap

fd1d_burgers_leap, a MATLAB code which solves the nonviscous time-dependent Burgers equation using finite differences and the leapfrog 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_leap
runs the program.

### Languages:

fd1d_burgers_leap 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 MATLAB code which evaluates an exact solution of the time-dependent 1d viscous burgers equation.

burgers_steady_viscous, a MATLAB code 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 code which solves the time-dependent viscous burgers equation using a finite difference discretization of the conservative form of the equation.

fd1d_advection_ftcs, a MATLAB code 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_burgers_lax, a MATLAB code 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_bvp, a MATLAB code which applies the finite difference method to a two point boundary value problem (bvp) in one spatial dimension.

fd1d_heat_explicit, a MATLAB code which uses the finite difference method and explicit time stepping to solve the time dependent heat equation in 1d.

fd1d_heat_implicit, a MATLAB code which uses the finite difference method and implicit time stepping to solve the time dependent heat equation in 1d.

fd1d_heat_steady, a MATLAB code which uses the finite difference method to solve the steady (time independent) heat equation in 1d.

fd1d_predator_prey, a MATLAB code which implements a finite difference algorithm for predator-prey system with spatial variation in 1d.

fd1d_wave, a MATLAB code which applies the finite difference method to solve the time-dependent wave equation in one spatial dimension.

### Reference:

1. Daniel Zwillinger,
Handbook of Differential Equations,