Setup Theseus.jl documentation

- Add docs/src/theseus.md with API reference for all integrator families
- Fix refs.bib: convert BibLaTeX fields (journaltitle, date) to BibTeX
  (journal, year), add missing comma to Kelley2022 key, remove urldate
  warnings
- Fix CI doctest step: use doctest(Theseus; manual=false) since Theseus
  does not have its own docs/src directory

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

Author: vchuravy

.github/workflows/Documentation.yml

@@ -36,7 +36,7 @@ jobs:
             DocMeta.setdocmeta!(Ariadne, :DocTestSetup, :(using Ariadne); recursive=true)
             DocMeta.setdocmeta!(Theseus, :DocTestSetup, :(using Theseus); recursive=true)
             doctest(Ariadne)
-            doctest(Theseus)
+            doctest(Theseus; manual=false)
           '
       - name: generate docs
         run: julia --project=docs docs/make.jl

docs/src/refs.bib

@@ -1,27 +1,21 @@
-@BOOK{Kelley2022
+@BOOK{Kelley2022,
   title     = {Solving nonlinear equations with iterative methods: Solvers and
                examples in Julia},
   author    = {Kelley, C T},
   publisher = {Society for Industrial and Applied Mathematics},
-  location  = {Philadelphia, PA},
-  date      = {2022-01},
+  year      = {2022},
   doi       = {10.1137/1.9781611977271},
   isbn      = {9781611977264,9781611977271},
-  urldate   = {2024-11-15},
-  language  = {en}
 }
 
 @BOOK{Kelley2003,
   title     = {Solving nonlinear equations with Newton's method},
   author    = {Kelley, C T},
   publisher = {Society for Industrial and Applied Mathematics},
-  location  = {Philadelphia, Pa.},
-  date      = {2003},
+  year      = {2003},
   doi       = {10.1137/1.9780898718898},
   isbn      = {9780898715460,9780898718898},
   series    = {Fundamentals of algorithms},
-  urldate   = {2024-11-12},
-  language  = {en}
 }
 
 @article{montoison-orban-2023,
@@ -36,65 +30,47 @@ @article{montoison-orban-2023
 }
 
 @ARTICLE{Kan2022-ko,
-  title        = {Extension of complex step finite difference method to
-                  Jacobian-free {Newton–Krylov​} method},
-  author       = {Kan, Ziyun and Song, Ningning and Peng, Haijun and Chen,
-                  Biaosong},
-  journaltitle = {Journal of computational and applied mathematics},
-  publisher    = {Elsevier BV},
-  volume       = {399},
-  issue        = {113732},
-  pages        = {113732},
-  date         = {2022-01-01},
-  doi          = {10.1016/j.cam.2021.113732},
-  issn         = {0377-0427,1879-1778},
-  urldate      = {2024-10-21},
-  language     = {en}
+  title   = {Extension of complex step finite difference method to
+             Jacobian-free {Newton--Krylov} method},
+  author  = {Kan, Ziyun and Song, Ningning and Peng, Haijun and Chen,
+             Biaosong},
+  journal = {Journal of Computational and Applied Mathematics},
+  volume  = {399},
+  pages   = {113732},
+  year    = {2022},
+  doi     = {10.1016/j.cam.2021.113732},
 }
 
 @ARTICLE{Hosea1996-xv,
-  title        = {Analysis and implementation of {TR}-{BDF2}},
-  author       = {Hosea, M E and Shampine, L F},
-  journaltitle = {Applied numerical mathematics: transactions of IMACS},
-  publisher    = {Elsevier BV},
-  volume       = {20},
-  issue        = {1-2},
-  pages        = {21--37},
-  date         = {1996-02-01},
-  doi          = {10.1016/0168-9274(95)00115-8},
-  issn         = {0168-9274,1873-5460},
-  urldate      = {2025-03-04},
-  language     = {en}
+  title   = {Analysis and implementation of {TR}-{BDF2}},
+  author  = {Hosea, M E and Shampine, L F},
+  journal = {Applied Numerical Mathematics},
+  volume  = {20},
+  number  = {1--2},
+  pages   = {21--37},
+  year    = {1996},
+  doi     = {10.1016/0168-9274(95)00115-8},
 }
 
 @ARTICLE{Bank1985-gh,
-  title        = {Transient simulation of silicon devices and circuits},
-  author       = {Bank, R E and Coughran, W M and Fichtner, W and Grosse, E H
-                  and Rose, D J and Smith, R K},
-  journaltitle = {IEEE transactions on electron devices},
-  publisher    = {Institute of Electrical and Electronics Engineers (IEEE)},
-  volume       = {32},
-  issue        = {10},
-  pages        = {1992--2007},
-  date         = {1985-10},
-  doi          = {10.1109/t-ed.1985.22232},
-  issn         = {0018-9383,1557-9646},
-  urldate      = {2025-05-27},
-  language     = {en}
+  title   = {Transient simulation of silicon devices and circuits},
+  author  = {Bank, R E and Coughran, W M and Fichtner, W and Grosse, E H
+             and Rose, D J and Smith, R K},
+  journal = {IEEE Transactions on Electron Devices},
+  volume  = {32},
+  number  = {10},
+  pages   = {1992--2007},
+  year    = {1985},
+  doi     = {10.1109/t-ed.1985.22232},
 }
 
 @ARTICLE{Bonaventura2021-za,
-  title        = {The {TR}-{BDF2} method for second order problems in structural
-                  mechanics},
-  author       = {Bonaventura, Luca and Mármol, Macarena Gómez},
-  journaltitle = {Computers \& mathematics with applications (Oxford, England:
-                  1987)},
-  publisher    = {Elsevier BV},
-  volume       = {92},
-  pages        = {13--26},
-  date         = {2021-06-15},
-  doi          = {10.1016/j.camwa.2021.03.037},
-  issn         = {0898-1221,1873-7668},
-  urldate      = {2025-05-27},
-  language     = {en}
+  title   = {The {TR}-{BDF2} method for second order problems in structural
+             mechanics},
+  author  = {Bonaventura, Luca and M{\'a}rmol, Macarena G{\'o}mez},
+  journal = {Computers \& Mathematics with Applications},
+  volume  = {92},
+  pages   = {13--26},
+  year    = {2021},
+  doi     = {10.1016/j.camwa.2021.03.037},
 }

docs/src/theseus.md

@@ -0,0 +1,68 @@
+# Theseus.jl
+
+Theseus.jl provides implicit and implicit-explicit (IMEX) time integration methods that use
+Ariadne.jl's Newton–Krylov solver internally.  All methods implement the
+[DifferentialEquations.jl integrator interface](https://docs.sciml.ai/DiffEqDocs/stable/basics/integrator/)
+and can be used with `ODEProblem` (and `SplitODEProblem` for IMEX).
+
+## Nonlinear Implicit Methods
+
+These single-step methods solve one nonlinear system per stage via Newton–Krylov.
+They accept an `ODEProblem` and the keyword argument `dt` (fixed time step).
+
+```@docs
+Theseus.ImplicitEuler
+Theseus.ImplicitMidpoint
+Theseus.ImplicitTrapezoid
+Theseus.TRBDF2
+```
+
+## Diagonally Implicit Runge–Kutta (DIRK) Methods
+
+DIRK methods use a lower-triangular Butcher tableau.  Each implicit stage requires
+one Newton–Krylov solve.  They accept an `ODEProblem`.
+
+```@docs
+Theseus.LobattoIIIA2
+Theseus.Crouzeix32
+Theseus.DIRK43
+```
+
+## Implicit–Explicit (IMEX) Runge–Kutta Methods
+
+IMEX methods split the right-hand side into a stiff part ``f_1`` and a non-stiff
+part ``f_2``.  They accept a `SplitODEProblem(f1!, f2!, u0, tspan)`.
+
+### Type I methods (Pareschi–Russo)
+
+```@docs
+Theseus.SP111
+Theseus.H222
+Theseus.SSP2222
+Theseus.SSP2322
+Theseus.SSP2332
+Theseus.SSP3332
+Theseus.SSP3433
+```
+
+### Type II methods (Ascher–Ruuth–Spiteri)
+
+```@docs
+Theseus.HT222
+Theseus.ARS111
+Theseus.ARS222
+Theseus.ARS233
+Theseus.ARS443
+```
+
+## Rosenbrock-W Methods
+
+Rosenbrock-W methods linearise the implicit system and solve one linear system
+(via a Krylov method) per stage instead of a full Newton solve.  The Jacobian
+approximation makes them *W methods*: the exact Jacobian is not required.
+They accept an `ODEProblem`.
+
+```@docs
+Theseus.SSPKnoth
+Theseus.ROS2
+```