ODE and PDE Solvers
Wolfram Research, Inc.
This talk looks into
NDSolve in some detail. Problems
arising from the numerical solution of ordinary differential equations will be explored,
including higher order and systems of equations, initial and boundary-value problems, and
stiffness. The current state of the numerical solver for partial differential equations is
outlined. The discretizations that are used and the current limits are also discussed.
Along the way, the various types of errors that inevitably arise are highlighted. These
include local, global, spatial, and temporal errors, and examples are used to explain how
they can be controlled.