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SciML · Aug 21, 2024 · db42e85 · db42e85
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diff --git a/lib/OrdinaryDiffEqExponentialRK/src/algorithms.jl b/lib/OrdinaryDiffEqExponentialRK/src/algorithms.jl
@@ -48,9 +48,15 @@ end
 
 const ETD1 = NorsettEuler # alias
 
+
+REF2 = """
+Hochbruck, M., & Ostermann, A. (2010). Exponential integrators. Acta Numerica, 19, 209-286. (https://doi.org/10.1017/S0962492910000048)
+"""
+
+
 for (Alg, Description, Ref) in [
-            (:Exprb32, "3rd order adaptive Exponential-Rosenbrock scheme.", "ref TBD"),
-            (:Exprb43, "4th order adaptive Exponential-Rosenbrock scheme.", "ref TBD")]
+            (:Exprb32, "3rd order adaptive Exponential-Rosenbrock scheme.", REF2),
+            (:Exprb43, "4th order adaptive Exponential-Rosenbrock scheme.", REF2)]
     @eval begin @doc generic_solver_docstring($Description,
                         $(string(Alg)),
                         "Semilinear ODE solver",
@@ -79,14 +85,26 @@ for (Alg, Description, Ref) in [
             iop)
     end
 end
+
+REF3 = """
+Hochbruck, M., Lubich, C., & Selhofer, H. (1998). Exponential integrators for large systems of differential equations. SIAM Journal on Scientific Computing, 19(5), 1552-1574. (https://doi.org/10.1137/S1064827595295337)
+"""
+
+REF4 = """
+Rainwater, G., & Tokman, M. (2016). A new approach to constructing efficient stiffly accurate EPIRK methods. Journal of Computational Physics, 323, 283-309. (https://doi.org/10.1016/j.jcp.2016.07.026)
+"""
+REF5 = """
+Tokman, M., Loffeld, J., & Tranquilli, P. (2012). New Adaptive Exponential Propagation Iterative Methods of Runge--Kutta Type. SIAM Journal on Scientific Computing, 34(5), A2650-A2669. (https://doi.org/10.1137/110849961)
+"""
+
 for (Alg, Description, Ref) in [
-    (:Exp4, "4th order EPIRK scheme.", "REF TBD")
-    (:EPIRK4s3A, "4th order EPIRK scheme with stiff order 4.", "REF TBD")
-    (:EPIRK4s3B, "4th order EPIRK scheme with stiff order 4.", "REF TBD")
-    (:EPIRK5s3, "5th order “horizontal” EPIRK scheme with stiff order 5. Broken.", "REF TBD")
-    (:EXPRB53s3, "5th order EPIRK scheme with stiff order 5.", "REF TBD")
-    (:EPIRK5P1, "5th order EPIRK scheme", "REF TBD")
-    (:EPIRK5P2, "5th order EPIRK scheme", "REF TBD")
+    (:Exp4, "4th order EPIRK scheme.", REF3)
+    (:EPIRK4s3A, "4th order EPIRK scheme with stiff order 4.", REF4)
+    (:EPIRK4s3B, "4th order EPIRK scheme with stiff order 4.", REF4)
+    (:EPIRK5s3, "5th order “horizontal” EPIRK scheme with stiff order 5. Broken.", REF4)
+    (:EXPRB53s3, "5th order EPIRK scheme with stiff order 5.", REF4)
+    (:EPIRK5P1, "5th order EPIRK scheme", REF5)
+    (:EPIRK5P2, "5th order EPIRK scheme", REF5)
     ]
     @eval begin
         @doc generic_solver_docstring($Description,

diff --git a/lib/OrdinaryDiffEqIMEXMultistep/src/algorithms.jl b/lib/OrdinaryDiffEqIMEXMultistep/src/algorithms.jl
@@ -1,5 +1,9 @@
 # IMEX Multistep methods
 
+@doc generic_solver_docstring("Description TBD",
+    "CNAB2",
+    "IMEX Multistep method.",
+    "REF TBD", "", "")
 struct CNAB2{CS, AD, F, F2, P, FDT, ST, CJ} <:
        OrdinaryDiffEqNewtonAlgorithm{CS, AD, FDT, ST, CJ}
     linsolve::F
@@ -21,6 +25,10 @@ function CNAB2(; chunk_size = Val{0}(), autodiff = Val{true}(), standardtag = Va
         extrapolant)
 end
 
+@doc generic_solver_docstring("TBD",
+    "CNLF2",
+    "IMEX Multistep method.",
+    "REF TBD", "", "")
 struct CNLF2{CS, AD, F, F2, P, FDT, ST, CJ} <:
        OrdinaryDiffEqNewtonAlgorithm{CS, AD, FDT, ST, CJ}
     linsolve::F

diff --git a/lib/OrdinaryDiffEqLinear/src/algorithms.jl b/lib/OrdinaryDiffEqLinear/src/algorithms.jl
@@ -1,30 +1,97 @@
 # Linear Methods
+REF1 = """
+@article{celledoni2014introduction,
+  title={An introduction to Lie group integrators--basics, new developments and applications},
+  author={Celledoni, Elena and Marthinsen, H{\aa}kon and Owren, Brynjulf},
+  journal={Journal of Computational Physics},
+  volume={257},
+  pages={1040--1061},
+  year={2014},
+  publisher={Elsevier}
+}
+"""
+REF2 = """
+@article{crouch1993numerical,
+  title={Numerical integration of ordinary differential equations on manifolds},
+  author={Crouch, Peter E and Grossman, R},
+  journal={Journal of Nonlinear Science},
+  volume={3},
+  pages={1--33},
+  year={1993},
+  publisher={Springer}
+}
+"""
+REF3 = """
+@article{blanes2000improved,
+  title={Improved high order integrators based on the Magnus expansion},
+  author={Blanes, Sergio and Casas, Fernando and Ros, Javier},
+  journal={BIT Numerical Mathematics},
+  volume={40},
+  number={3},
+  pages={434--450},
+  year={2000},
+  publisher={Springer}
+}
+"""
+REF4 = """
+@article{blanes2009magnus,
+  title={The Magnus expansion and some of its applications},
+  author={Blanes, Sergio and Casas, Fernando and Oteo, Jose-Angel and Ros, Jos{\'e}},
+  journal={Physics reports},
+  volume={470},
+  number={5-6},
+  pages={151--238},
+  year={2009},
+  publisher={Elsevier}
+}
+"""
+REF5 = """
+@article{hairer2011solving,
+  title={Solving differential equations on manifolds},
+  author={Hairer, Ernst},
+  journal={Lecture notes},
+  year={2011}
+}
+"""
+REF6 = """
+@article{jackiewicz2000construction,
+  title={Construction of Runge--Kutta methods of Crouch--Grossman type of high order},
+  author={Jackiewicz, Zdzislaw and Marthinsen, Arne and Owren, Brynjulf},
+  journal={Advances in Computational Mathematics},
+  volume={13},
+  pages={405--415},
+  year={2000},
+  publisher={Springer}
+}
+"""
 
 for (Alg, Description, Ref) in [
     (:MagnusMidpoint, "Second order Magnus Midpoint method.", "ref TBD"),
     (:MagnusLeapfrog, "Second order Magnus Leapfrog method.", "ref TBD"),
-    (:LieEuler, "description", "ref TBD"),
-    (:MagnusGauss4, "Fourth order Magnus method approximated using a two stage Gauss quadrature.", "ref TBD"),
-    (:MagnusNC6, "Sixth order Magnus method approximated using Newton-Cotes quadrature.", "ref TBD"),
-    (:MagnusGL6, "Sixth order Magnus method approximated using Gauss-Legendre quadrature.", "ref TBD"),
-    (:MagnusGL8, "Eighth order Magnus method approximated using Newton-Cotes quadrature.", "ref TBD"),
-    (:MagnusNC8, "Eighth order Magnus method approximated using Gauss-Legendre quadrature.", "ref TBD"),
-    (:MagnusGL4, "Fourth order Magnus method approximated using Gauss-Legendre quadrature.", "ref TBD"),
-    (:RKMK2, "Second order Runge–Kutta–Munthe-Kaas method.", "ref TBD"),
-    (:RKMK4, "Fourth order Runge–Kutta–Munthe-Kaas method.", "ref TBD"),
-    (:LieRK4, "Fourth order Lie Runge-Kutta method.", "ref TBD"),
-    (:CG2, "Second order Crouch–Grossman method.", "ref TBD"),
-    (:CG3, "Third order Crouch-Grossman method.", "ref TBD"),
-    (:CG4a, " Fourth order Crouch-Grossman method.", "ref TBD")]
+    (:LieEuler, "description", REF1),
+    (:MagnusGauss4, "Fourth order Magnus method approximated using a two stage Gauss quadrature.", REF5),
+    (:MagnusNC6, "Sixth order Magnus method approximated using Newton-Cotes quadrature.", REF3),
+    (:MagnusGL6, "Sixth order Magnus method approximated using Gauss-Legendre quadrature.", REF3),
+    (:MagnusGL8, "Eighth order Magnus method approximated using Newton-Cotes quadrature.", REF3),
+    (:MagnusNC8, "Eighth order Magnus method approximated using Gauss-Legendre quadrature.", REF3),
+    (:MagnusGL4, "Fourth order Magnus method approximated using Gauss-Legendre quadrature.", REF4),
+    (:RKMK2, "Second order Runge–Kutta–Munthe-Kaas method.", REF1),
+    (:RKMK4, "Fourth order Runge–Kutta–Munthe-Kaas method.", REF1),
+    (:LieRK4, "Fourth order Lie Runge-Kutta method.", REF1),
+    (:CG2, "Second order Crouch–Grossman method.", REF1),
+    (:CG3, "Third order Crouch-Grossman method.", REF2),
+    (:CG4a, " Fourth order Crouch-Grossman method.", REF6)]
     @eval begin
         @doc generic_solver_docstring($Description,
             $(string(Alg)),
             "Semilinear ODE solver",
             $Ref,
             """
-            - `krylov`: TBD
-            - `m`: TBD
-            - `iop`: TBD
+            - `krylov`: Determines whether Krylov approximation or operator caching is used, the latter only available for semilinear problems.
+                `krylov=true` is much faster for larger systems and is thus recommended whenever there are >100 ODEs.
+            - `m`: Controls the size of Krylov subspace.
+            - `iop`: If not zero, determines the length of the incomplete orthogonalization procedure (IOP).
+                    Note that if the linear operator/Jacobian is hermitian, then the Lanczos algorithm will always be used and the IOP setting is ignored.
             """,
             """
             krylov = false,
@@ -55,7 +122,11 @@ struct CayleyEuler <: OrdinaryDiffEqAlgorithm end
 @doc generic_solver_docstring("Exact solution formula for linear, time-independent problems.",
     "LinearExponential",
     "Semilinear ODE solver",
-    "ref TBD",
+    "@book{strogatz2018nonlinear,
+    title={Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering},
+    author={Strogatz, Steven H},
+    year={2018},
+    publisher={CRC press}}",
     """
     - `krylov`:
         - `:off`: cache the operator beforehand. Requires Matrix(A) method defined for the operator A.