BURGERS_SOLUTION
Exact Solution of Time Dependent 1D Viscous Burgers Equation
BURGERS_SOLUTION
is a Python library which
evaluates an exact solution 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
for 1.0 < x < +1.0, and 0.0 < t.
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];
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.py,
evaluates solution #1 to the Burgers equation.

burgers_viscous_time_exact2.py,
evaluates solution #2 to the Burgers equation.

hermite_ek_compute.py,
computes a GaussHermite quadrature rule.

imtqlx.py,
diagonalizes a symmetric tridiagonal matrix.

r8_epsilon.py,
returns the machine epsilon value.

r8_gamma.py,
evaluates the gamma function.

r8_sign.py,
returns the sign of an R8.

r8mat_print.py,
prints an R8MAT.

r8mat_print_some.py,
prints some of an R8MAT.

r8mat_write.py,
writes an R8MAT file.

r8vec_print.py,
prints an R8VEC.

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

burgers_solution_test.py,
calls all the tests.

burgers_solution_test.sh,
runs all the tests.

burgers_solution_test_output.txt,
the output file.

burgers_solution_test01.txt,
a data file of solution #1 values for 1 <= x <= +1,
0 <= t <= 3/pi, using 11 grid points in x and in t.

burgers_solution_test02.txt,
a data file of solution #1 values for 1 <= x <= +1,
0 <= t <= 3/pi, using 41 grid points in x and in t.

burgers_solution_test03.txt,
a data file of solution #2 values for 0 <= x <= 2 Pi,
0 <= t <= 1, using 11 grid points in x and in t.

burgers_solution_test04.txt,
a data file of solution #2 values for 0 <= x <= 2 Pi,
0 <= t <= 1, using 41 grid points in x and in t.
You can go up one level to
the Python source codes.
Last revised on 27 September 2015.