 Differential
Equations
Maple 10 uses new sophisticated functions to represent solutions
to many formerly unsolvable families of linear and nonlinear
differential equations. Original computational algorithms have
been developed by the Maplesoft research team–the most
important development in ordinary differential equations (ODEs)
in the last four Maple releases.
The following is a list of some of the improvements for finding
exact solutions of ODEs and partial differential equations (PDEs),
and systems of ODEs and PDEs.
- Newly developed solving algorithms
for certain classes of Abel type ODEs, Riccati
type ODEs, and Heun function solutions
- Newly developed solving algorithms
for computing different types of Traveling Wave
Solutions for PDEs and PDE systems
- Newly added algorithms for
computing Liouvillian solutions and for solving
a general class of ODEs that can be mapped to
Abel type
- Improved algorithms for computing
doubly periodic solutions for second order linear
ODEs
Maple 10 also includes improvements
and additions to the DEtools and PDEtools packages.
- Nine new commands added to DEtools:
- Compute homomorphisms
between the solution spaces of two linear
differential operators
- Compute particular solutions
to linear equations in cases where the
general solution cannot be found
- Handle differential
rational normal forms and hyperexponential
functions
- New differential polynomial
extensions added to PDEtools for
differential polynomial forms. The interactive
ODE Analyzer takes full advantage of the new
algorithms.
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