First features

Author: SKopecz

paper/paper.md

@@ -38,7 +38,11 @@ TODO
 
 # Features
 
-TODO
+- Production-destruction problems `PDSProblem` and `ConservativePDSProblem`, including conversions to standard ODEProblems from `DifferentialEquations.jl`
+- Modified Patankar methods `MPE`, `MPRK22`, `MPRK43I` and `MPRK43II` of Kopecz and Meister
+- SSP MPRK methods `SSPMPRK22` and `SSPMPRK43` of Huang, Zhao and Shu
+- `MPDeC` methods of Öffner and Torlo
+- Extensions of the above schemes for non-conservative and non-autonomous production-destruction systems, mostly using adaptive time stepping
 
 
 # Related research and software
@@ -55,12 +59,10 @@ All implemented schemes were originally introduced for conservative production-d
 Readers interested in additional theoretical background and further properties of the implemented schemes are referred to the following papers: @kopeczmeister2019, @izgin2022stability1, @izgin2022stability2, @huang2023, @torlo2022, @izginoeffner2023
 
 Existing software libraries do not have a strong focus on unconditional positivity and, to the authors' knowledge, there is no other software library which offers MPRK schemes. 
-
 A common strategy to obtain nonnegative solutions used in the `PositiveDomain` callback of `Differentialequtions'jl` or the commercial package `Matlab` is described by @Shampine2005. In this approach negative components of approximate solutions that have been accepted by the adaptive time stepping algorithm are set to zero.
-
 Another possibility is to reduce the chosen time step size beyond accuracy considerations until a non-negative approximation is calculated. This can be achieved in `DifferentialEquations.jl` using the solver option `isoutofdomain`.
 
-Some papers on MPRK schemes offer supplementary codes. However, these are mainly small scripts for the reproduction of results shown in the papers and are not intended as software libraries.
+In addition, some papers on MPRK schemes offer supplementary codes. However, these are mainly small scripts for the reproduction of results shown in the papers and are not intended as software libraries.
 
 
 TODO