fd1d_burgers_leap, a Fortran77 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, a Fortran77 library which evaluates an exact solution of the time-dependent 1D viscous Burgers equation.
FD1D_BURGERS_LAX, a Fortran77 program which applies the finite difference method and the Lax-Wendroff method to solve the non-viscous time-dependent Burgers equation in one spatial dimension.
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FD1D_HEAT_EXPLICIT, a Fortran77 program which uses the finite difference method and explicit time stepping to solve the time dependent heat equation in 1D.
FD1D_HEAT_IMPLICIT, a Fortran77 program which uses the finite difference method and implicit time stepping to solve the time dependent heat equation in 1D.
FD1D_HEAT_STEADY, a Fortran77 program which uses the finite difference method to solve the steady (time independent) heat equation in 1D.
FD1D_PREDATOR_PREY, a Fortran77 program which implements a finite difference algorithm for predator-prey system with spatial variation in 1D.
FD1D_WAVE, a Fortran77 program which applies the finite difference method to solve the time-dependent wave equation utt = c * uxx in one spatial dimension.