Optimal
Methods
 For
nonlinear/nonautonomous systems:
 Explicit methods
 Implicit methods
 For linear, autonomous systems:
 Explicit methods
 Implicit methods

Strong
stability preserving methods (also known as total variation
diminishing, contractivity preserving, or monotonicity preserving
methods), are numerical methods for solving ordinary differential
equations. They were developed for the time integration of
semidiscretizations of hyperbolic conservation laws. The exact
solutions of scalar conservation laws have the property that their
total variation does not increase in time. Semidiscretizations are
often designed so that their discrete solutions also have this
property under forward Euler integration. SSP methods are higher
order methods that also preserve this property. Because of this, they
were originally referred to as TVD methods. However, they have the
stronger property that they will preserve any convex functional bound
(such as, e.g., positivity) that is satisfied under forward Euler
integration. This page is a repository for
information on SSP methods, including coefficients of optimal
methods.
