  We present the algorithms for three popular methods: F-expansion, modified
F-expansion, and first integral methods to automatically get closed-form
traveling-wave solutions of nonlinear partial differential equations (NLPDEs).
We generalize and improve the methods. The proposed algorithms are manageable,
straightforward, and powerful tools providing a high-performance evaluation of
the exact solutions of nonlinear ordinary differential equations (NLODEs) and
NLPDEs. For differential equations with parameters, the new algorithms
determine the conditions on the parameters to obtain exact solutions. The
algorithms show solutions to a wide variety of NLODEs and NLPDEs, both
integrable and non-integrable. It can solve NLODEs and NLPDEs that contain
complex functions. The algorithms are implemented in a C++ library named
GiNaCDE. The efficiency and effectiveness of the algorithms are demonstrated by
some examples with the help of GiNaCDE. The output results tally with the
previously known results, and in some cases, new exact traveling-wave solutions
are explicitly obtained. Use of the library, implementation issues, scope,
limitations, and future extensions of the software are addressed.
