Added DIRK methods and testsets from Hairer/Wanner book

[MagalieHeinrich]

Added DIRK methods and testsets from E. Hairer, G. Wanner. Solving ordinary differential equations II: Stiff and Differential-Algebraic Problems.

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[MarcoArtiano]

Thanks! I left a few suggestions after a first quick review.

[ranocha]

Thanks! I just have a few minor additional suggestions.

[ranocha]

@MagalieHeinrich I left some additional comments. Please incorporate them and ping me afterward.

[MarcoArtiano]

Thanks, I've left some other minor comments.

[MarcoArtiano]

I don't understand the comment here. There was a typo in the Hairer-Wanner book?

[MagalieHeinrich]

I removed the comment.
I made a typo while typing from the book. When checking, I put the comment. I then forgot to remove the comment. That's why it was there.

[MagalieHeinrich]

@ranocha I added your and @MarcoArtiano 's suggested changes.

"M. Crouzeix. Sur l’approximation des équations différentielles opérationnelles linéaires par des méthodes de Runge-Kutta.
Thèse d'état, Univ. Paris 6 192pp, 1975."

failed the spell check saying "sur" should be "sure". I suppose thats because the spell check checks for english. Any suggestions?

[ranocha]

You can add a line sur = "sur" to https://github.com/NumericalMathematics/Ariadne.jl/blob/main/.typos.toml

[github-actions]

Your PR requires formatting changes to meet the project's style guidelines.
Please consider running Runic (git runic main) to apply these changes.

Click here to view the suggested changes.

diff --git a/libs/Theseus/src/dirk/tableau.jl b/libs/Theseus/src/dirk/tableau.jl
index 90b11f4..652029e 100644
--- a/libs/Theseus/src/dirk/tableau.jl
+++ b/libs/Theseus/src/dirk/tableau.jl
@@ -117,16 +117,16 @@ struct CooperSayfy5 <: DIRK{5} end
 function RKTableau(alg::CooperSayfy5, RealT)
     nstage = 5
     sqrt6 = sqrt(convert(RealT, 6))
-    
+
     γ = (6 - sqrt6) / 10
-    
+
     a = zeros(RealT, nstage, nstage)
-    
+
     a[1, 1] = γ
 
     a[2, 1] = (6 + 5 * sqrt6) / 14
     a[2, 2] = γ
-    
+
     a[3, 1] = (888 + 607 * sqrt6) / 2850
     a[3, 2] = (126 - 161 * sqrt6) / 1425
     a[3, 3] = γ
@@ -141,21 +141,21 @@ function RKTableau(alg::CooperSayfy5, RealT)
     a[5, 3] = (1329 - 544 * sqrt6) / 2500
     a[5, 4] = (-96 + 131 * sqrt6) / 625
     a[5, 5] = γ
-    
+
     b = zeros(RealT, nstage)
     b[1] = 0
     b[2] = 0
     b[3] = 1 // 9
     b[4] = (16 - sqrt6) / 36
     b[5] = (16 + sqrt6) / 36
-    
+
     c = zeros(RealT, nstage)
     c[1] = γ
     c[2] = (6 + 9 * sqrt6) / 35
-    c[3] = 1 
+    c[3] = 1
     c[4] = (4 - sqrt6) / 10
     c[5] = (4 + sqrt6) / 10
-    
+
     return DIRKButcher(a, b, c)
 end
 
@@ -173,23 +173,23 @@ struct HairerWannerSDIRK4 <: DIRK{5} end
 function RKTableau(alg::HairerWannerSDIRK4, RealT)
     nstage = 5
     a = zeros(RealT, nstage, nstage)
-    
+
     γ = 1 // 4
-    
+
     a[1, 1] = γ
-    
+
     a[2, 1] = 1 // 2
     a[2, 2] = γ
-    
+
     a[3, 1] = 17 // 50
     a[3, 2] = -1 // 25
     a[3, 3] = γ
-    
+
     a[4, 1] = 371 // 1360
     a[4, 2] = -137 // 2720
     a[4, 3] = 15 // 544
     a[4, 4] = γ
-    
+
     a[5, 1] = 25 // 24
     a[5, 2] = -49 // 48
     a[5, 3] = 125 // 16
@@ -202,14 +202,14 @@ function RKTableau(alg::HairerWannerSDIRK4, RealT)
     b[3] = 125 // 16
     b[4] = -85 // 12
     b[5] = 1 // 4
-    
+
     c = zeros(RealT, nstage)
     c[1] = 1 // 4
     c[2] = 3 // 4
     c[3] = 11 // 20
     c[4] = 1 // 2
     c[5] = 1
-    
+
     return DIRKButcher(a, b, c)
 end
 
@@ -228,11 +228,11 @@ A fourth-order, three-stage, L-stable SDIRK method.
 struct CrouzeixRaviart34 <: DIRK{3} end
 function RKTableau(alg::CrouzeixRaviart34, RealT)
     nstage = 3
-    
+
     sqrt3 = sqrt(convert(RealT, 3))
     γ = (1 / sqrt3) * cospi(one(RealT) / 18) + 1 // 2
     δ = 1 / (6 * (2 * γ - 1)^2)
-    
+
     a = zeros(RealT, nstage, nstage)
 
     a[1, 1] = γ
@@ -243,18 +243,18 @@ function RKTableau(alg::CrouzeixRaviart34, RealT)
     a[3, 1] = 2 * γ
     a[3, 2] = 1 - 4 * γ
     a[3, 3] = γ
-    
+
     b = zeros(RealT, nstage)
     b[1] = δ
     b[2] = 1 - 2 * δ
     b[3] = δ
-    
+
     c = zeros(RealT, nstage)
     c[1] = γ
     c[2] = 1 // 2
     c[3] = 1 - γ
-    
+
     return DIRKButcher(a, b, c)
 end
-    
+
 
diff --git a/libs/Theseus/test/convergence.jl b/libs/Theseus/test/convergence.jl
index 4e2f9d1..e32333f 100644
--- a/libs/Theseus/test/convergence.jl
+++ b/libs/Theseus/test/convergence.jl
@@ -84,7 +84,7 @@ end
             eoc = compute_eoc(dts, errors)
             @test isapprox(eoc, order; atol = 0.1)
         end
-    
+
         @testset "CooperSayfy5" begin
             alg = Theseus.CooperSayfy5()
             order = 5

[ranocha]

Thanks