Merge pull request SciML#2273 from Shreyas-Ekanathan/master

Implement 7th order RadauIIA method

Author: ChrisRackauckas

src/OrdinaryDiffEq.jl

@@ -415,7 +415,7 @@ export FunctionMap, Euler, Heun, Ralston, Midpoint, RK4, ExplicitRK, OwrenZen3,
        FRK65, PFRK87,
        RKM, MSRK5, MSRK6, Stepanov5, SIR54, QPRK98, PSRK4p7q6, PSRK3p6q5, PSRK3p5q4
 
-export RadauIIA3, RadauIIA5
+export RadauIIA3, RadauIIA5, RadauIIA7
 
 export ImplicitEuler, ImplicitMidpoint, Trapezoid, TRBDF2, SDIRK2, SDIRK22,
        Kvaerno3, KenCarp3, Cash4, Hairer4, Hairer42, SSPSDIRK2, Kvaerno4,

src/alg_utils.jl

@@ -176,7 +176,7 @@ qmin_default(alg::DP8) = 1 // 3
 qmax_default(alg::Union{OrdinaryDiffEqAlgorithm, DAEAlgorithm}) = 10
 qmax_default(alg::CompositeAlgorithm) = minimum(qmax_default.(alg.algs))
 qmax_default(alg::DP8) = 6
-qmax_default(alg::Union{RadauIIA3, RadauIIA5}) = 8
+qmax_default(alg::Union{RadauIIA3, RadauIIA5, RadauIIA7}) = 8
 
 function has_chunksize(alg::OrdinaryDiffEqAlgorithm)
     return alg isa Union{OrdinaryDiffEqExponentialAlgorithm,
@@ -441,6 +441,7 @@ alg_order(alg::TanYam7) = 7
 alg_order(alg::TsitPap8) = 8
 alg_order(alg::RadauIIA3) = 3
 alg_order(alg::RadauIIA5) = 5
+alg_order(alg::RadauIIA7) = 7
 alg_order(alg::ImplicitEuler) = 1
 alg_order(alg::RKMK2) = 2
 alg_order(alg::RKMK4) = 4

src/algorithms.jl

@@ -995,6 +995,60 @@ function RadauIIA5(; chunk_size = Val{0}(), autodiff = Val{true}(),
 end
 TruncatedStacktraces.@truncate_stacktrace RadauIIA5
 
+"""
+@article{hairer1999stiff,
+title={Stiff differential equations solved by Radau methods},
+author={Hairer, Ernst and Wanner, Gerhard},
+journal={Journal of Computational and Applied Mathematics},
+volume={111},
+number={1-2},
+pages={93--111},
+year={1999},
+publisher={Elsevier}
+}
+
+RadauIIA7: Fully-Implicit Runge-Kutta Method
+An A-B-L stable fully implicit Runge-Kutta method with internal tableau complex basis transform for efficiency.
+"""
+struct RadauIIA7{CS, AD, F, P, FDT, ST, CJ, Tol, C1, C2, StepLimiter} <:
+    OrdinaryDiffEqNewtonAdaptiveAlgorithm{CS, AD, FDT, ST, CJ}
+    linsolve::F
+    precs::P
+    smooth_est::Bool
+    extrapolant::Symbol
+    κ::Tol
+    maxiters::Int
+    fast_convergence_cutoff::C1
+    new_W_γdt_cutoff::C2
+    controller::Symbol
+    step_limiter!::StepLimiter
+end
+
+function RadauIIA7(; chunk_size = Val{0}(), autodiff = Val{true}(),
+    standardtag = Val{true}(), concrete_jac = nothing,
+    diff_type = Val{:forward},
+    linsolve = nothing, precs = DEFAULT_PRECS,
+    extrapolant = :dense, fast_convergence_cutoff = 1 // 5,
+    new_W_γdt_cutoff = 1 // 5,
+    controller = :Predictive, κ = nothing, maxiters = 10, smooth_est = true,
+    step_limiter! = trivial_limiter!)
+RadauIIA7{_unwrap_val(chunk_size), _unwrap_val(autodiff), typeof(linsolve),
+    typeof(precs), diff_type, _unwrap_val(standardtag), _unwrap_val(concrete_jac),
+    typeof(κ), typeof(fast_convergence_cutoff),
+    typeof(new_W_γdt_cutoff), typeof(step_limiter!)}(linsolve,
+    precs,
+    smooth_est,
+    extrapolant,
+    κ,
+    maxiters,
+    fast_convergence_cutoff,
+    new_W_γdt_cutoff,
+    controller,
+    step_limiter!)
+end
+TruncatedStacktraces.@truncate_stacktrace RadauIIA7
+
+
 ################################################################################
 
 # SDIRK Methods