Differential
Equations Solving
Improvements
to solvers
for ordinary
differential
equations
(ODEs), partial
differential
equations
(PDEs), and
differential
algebraic
equations
(DAEs) continue
to strengthen
Maple’s world-leading
position
in numeric
and symbolic
differential
equation
solving.
Exact Solutions
Ordinary
Differential
Equations
(ODEs) and
Partial Differential
Equations
(PDEs)
- New
algorithms
for solving
entire classes
of 1st and
2nd order
non-linear
ODEs and
3rd order
linear ODEs
for which
no systematic
algorithms
have previously
existed
- New transformation techniques for
converting equations into forms that Maple can solve;
these transformations make it possible for Maple
to find solutions to many equations for which there
was previously no known solution
- New tools for working with partial
differential equations (PDEs), including commands
for working with Euler’s operator, conserved
currents, and generalized integrating factors, and
for computing the general solution for some
linear PDE families by using Laplace invariants
Numeric Solutions
Differential
Equations
(DEs) and
Differential
Algebraic
Equations
(DAEs)
Numeric solutions to initial value problems
with ordinary differential equations (ODE IVP) and
differential algebraic equations (DAE IVP) have many
new properties:
- The
ability to
handle user-defined
events: when
the event
occurs, user-defined
actions can
be performed
or a new
event triggered
- Parametric problem definition: a
procedure can be formed for a whole class of ODEs
or DAEs, then parameters can be adjusted, and different
solutions obtained interactively, without the need
to set up the problem every time
- Definition of discrete variables
as part of the problem description: when combined
with events, discrete variables can be used to handle
stopping criteria, reset conditions, zero-order
holds, and most other events that occur in ODE and
DAE system simulation
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