jburkardt

FD1D_BURGERS_LEAP\ Finite Difference Non-viscous Burgers Equation, Leapfrog Method {#fd1d_burgers_leap-finite-difference-non-viscous-burgers-equation-leapfrog-method align=”center”} ===============================================================

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FD1D_BURGERS_LEAP is a C++ program 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: {#usage align=”center”}

fd1d_burgers_leap

runs the program.

Licensing: {#licensing align=”center”}

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages: {#languages align=”center”}

FD1D_BURGERS_LEAP is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs: {#related-data-and-programs align=”center”}

BURGERS, a dataset directory which contains some solutions to the viscous Burgers equation.

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

FD1D_BURGERS_LAX, a C++ 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.

FD1D_BVP, a C++ program which applies the finite difference method to a two point boundary value problem in one spatial dimension.

FD1D_HEAT_EXPLICIT, a C++ program which uses the finite difference method and explicit time stepping to solve the time dependent heat equation in 1D.

FD1D_HEAT_IMPLICIT, a C++ program which uses the finite difference method and implicit time stepping to solve the time dependent heat equation in 1D.

FD1D_HEAT_STEADY, a C++ program which uses the finite difference method to solve the steady (time independent) heat equation in 1D.

FD1D_WAVE, a C++ program which applies the finite difference method to solve the time-dependent wave equation utt = c * uxx in one spatial dimension.

Reference: {#reference align=”center”}

1. Daniel Zwillinger,\ Handbook of Differential Equations,\ Academic Press, 1997,\ ISBN: 0127843965,\ LC: QA371.Z88.

Source Code: {#source-code align=”center”}

• fd1d_burgers_leap.cpp, the source code.

Examples and Tests: {#examples-and-tests align=”center”}

• fd1d_burgers_leap_output.txt, the output file.

List of Routines: {#list-of-routines align=”center”}

• FD1D_BURGERS_LEAP solves the nonviscous Burgers equation using leapfrogging.
• R8VEC_EVEN returns an R8VEC of evenly spaced values.
• REPORT prints or plots or saves the data at the current time step.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• U_A sets the boundary condition for U at A.
• U_B sets the boundary condition for U at B.
• U_INIT sets the initial condition for U.

You can go up one level to the C++ source codes.

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Last revised on 18 August 2010.