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