BURGERS_SOLUTION
Exact Solutions of Time Dependent 1D Viscous Burgers Equation
BURGERS_SOLUTION
is a MATLAB library which
evaluates exact solutions of the timedependent 1D viscous Burgers equation.
The form of the Burgers equation considered here is:
du du d^2 u
 + u *  = nu * 
dt dx dx^2
Licensing:
The computer code and data files described and made available on this
web page are distributed under
the GNU LGPL license.
Languages:
BURGERS_SOLUTION is available in
a C version and
a C++ version and
a FORTRAN77 version and
a FORTRAN90 version and
a MATLAB version and
a Python version.
Related Data and Programs:
BURGERS,
a dataset directory which
contains 40 solutions of the Burgers equation in one space dimension and time,
at equally spaced times from 0 to 1, with values
at 41 equally spaced nodes in [0,1];
BURGERS_STEADY_VISCOUS,
a MATLAB library which
solves the steady (timeindependent) 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.
FD1D_BURGERS_LAX,
a MATLAB program which
applies the finite difference method and the LaxWendroff method
to solve the nonviscous Burgers equation
in one spatial dimension and time.
FD1D_BURGERS_LEAP,
a MATLAB program which
applies the finite difference method and the leapfrog approach
to solve the nonviscous Burgers equation in one spatial dimension and time.
Reference:

Claude Basdevant, Michel Deville, Pierre Haldenwang, J Lacroix,
J Ouazzani, Roger Peyret, Paolo Orlandi, Anthony Patera,
Spectral and finite difference solutions of the Burgers equation,
Computers and Fluids,
Volume 14, Number 1, 1986, pages 2341.
Source Code:

burgers_viscous_time_exact1.m,
evaluates exact solution #1 to the Burgers equation.

burgers_viscous_time_exact2.m,
evaluates exact solution #2 to the Burgers equation.

hermite_ek_compute.m,
computes a GaussHermite quadrature rule.

imtqlx.m,
diagonalizes a symmetric tridiagonal matrix.

r8_sign.m,
returns the sign of an R8.

r8mat_print.m,
prints an R8MAT.

r8mat_print_some.m,
prints some of an R8MAT.

r8mat_write.m,
writes an R8MAT file.

r8vec_print.m,
prints an R8VEC.

timestamp.m,
prints the current YMDHMS date as a time stamp.
Examples and Tests:

burgers_solution_test.m,
calls all the tests.

burgers_solution_test01.m,
considers exact solution #1 for 11 grid points in x and t.

burgers_solution_test01.txt,
a data file using 11 grid points in x and in t.

burgers_solution_test01.png,
an image of U(X,T) by MATLAB's surf() command.

burgers_solution_test02.m,
considers exact solution #1 for 41 grid points in x and t.

burgers_solution_test02.txt,
a data file using 41 grid points in x and in t.

burgers_solution_test02.png,
an image of U(X,T) by MATLAB's surf() command.

burgers_solution_test03.m,
considers exact solution #2 for 11 grid points in x and t.

burgers_solution_test03.txt,
a data file using 11 grid points in x and in t.

burgers_solution_test03.png,
an image of U(X,T) by MATLAB's surf() command.

burgers_solution_test04.m,
considers exact solution #2 for 41 grid points in x and t.

burgers_solution_test04.txt,
a data file using 41 grid points in x and in t.

burgers_solution_test04.png,
an image of U(X,T) by MATLAB's surf() command.

burgers_solution_test_output.txt,
the output file.
You can go up one level to
the MATLAB source codes.
Last revised on 24 September 2015.