fd1d_burgers_leap, an Octave code which solves the nonviscous time-dependent Burgers equation using the finite difference method (FDM) and the leapfrog 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.
fd1d_burgers_leapruns the program.
The computer code and data files described and made available on this web page are distributed under the MIT license
fd1d_burgers_leap is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version.
burgers, a dataset directory which contains some solutions to the viscous Burgers equation.
burgers_solution, an Octave code which evaluates an exact solution of the time-dependent 1d viscous Burgers equation.
burgers_steady_viscous, an Octave 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, an Octave code which solves the time-dependent viscous Burgers equation using a finite difference discretization of the conservative form of the equation.
fd1d_advection_ftcs, an Octave code which applies the finite difference method (FDM) 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, an Octave code which applies the finite difference method (FDM) and the Lax-Wendroff method to solve the non-viscous time-dependent Burgers equation in one spatial dimension.
fd1d_bvp, an Octave code which applies the finite difference method to a two point boundary value problem (BVP) in one spatial dimension.
fd1d_heat_explicit, an Octave code which uses the finite difference method and explicit time stepping to solve the time dependent heat equation in 1d.
fd1d_heat_implicit, an Octave code which uses the finite difference method and implicit time stepping to solve the time dependent heat equation in 1d.
fd1d_heat_steady, an Octave code which uses the finite difference method to solve the steady (time independent) heat equation in 1d.
fd1d_predator_prey, an Octave code which implements a finite difference algorithm for predator-prey system with spatial variation in 1d.
fd1d_wave, an Octave code which applies the finite difference method to solve the time-dependent wave equation in one spatial dimension.