/*! \defgroup ODESolver ODE Solver Library

This ODE solver library has been designed with an implicit first-order
quasilinear ODE in mind. However, it is in principle not restricted to such a
kind of equation, but can be extended to also solve other equation types. In
particular it is possible to introduce equation types that are no ODEs, but are
nonlinear equations without time derivative terms.

The aim of the library's design is being able to formulate FEM processes without
having to care which time discretization scheme and which nonlinear iteration
method will be used to solve it.

The library offers different time discretization schemes, cf. \ref
concept_time_discretization "the conceputal remarks on them", namely the forward
and backward Euler and Crank-Nicolson methods and Backward Differentiation
Formulas. The design follows Gear's method, which also underlies the DASSL
algorithm of Petzold et al., cf. Differential-algebraic equations article,
section [Numerical methods/Direct discretization]
(http://www.scholarpedia.org/article/Differential-algebraic_equations#Numerical_methods.2FDirect_discretization)
\cite Campbell:2008.

A rough overview over the interplay between the various parts of this library is
given in the image below. Therein red symbols indicate which classes \e own
which matrices or vectors (for the meaning of the different symbols refer to the
documentation of the respective classes). The word \e own should not be taken
too strict in the sense of C++ member ownership, although currently it is
implemented as such; but in the future this implementation detail might change.
Rather \e own means that the class is in charge of the respective matrix or
vector, i.e., it can read from and write to it or pass it on to functions; or in
other words: The class knows about the meaning of that matrix/vector. Note that
only matrices and vectors that describe some proper state of the respective
classes are shown; those storing only intermediate computations have been
omitted from the image.

\image html  ode-solver-concept.png "Interplay of the different parts of the ODE
solver library at the example of a first-order implicit quasilinear ODE." \image
latex ode-solver-concept.pdf "Interplay of the different parts of the ODE solver
library at the example of a first-order implicit quasilinear ODE."

In the ODE solver library the instances of some classes can work together with
several instances of other classes throughout there lifetime, whereas they have
a strict one-to-one correspondence to objects of some different type. Those
relations are given in the following table.

Class 1                  | Class 2            | Relation | Remarks
-----------------------: | :----------------- | :------: | :----------
TimeDiscretizedODESystem | ODESystem          | 1:1      | the ODESystem
represents part of the state of the TimeDiscretizedODESystem
TimeDiscretizedODESystem | TimeDiscretization | 1:1      | analogous for the
TimeDiscretization TimeDiscretizedODESystem | MatrixTranslator   | 1:1      |
analogous for the MatrixTranslator NonlinearSolver          | NonlinearSystem |
1:n      | a nonlinear solver can solve various equations, one after the other
LinearSolver             | NonlinearSolver    | 1:n      | various
NonlinearSolver's can share the same LinearSolver


*/