Try using state from beginning of step as guess for implicit solver

Author: dennisYatunin

docs/src/dev/report_gen.jl

@@ -4,8 +4,8 @@ using InteractiveUtils: subtypes
 
 ENV["GKSwstype"] = "nul" # avoid displaying plots
 
-include(joinpath(@__DIR__, "..", "plotting_utils.jl"))
 include(joinpath(pkgdir(ClimaTimeSteppers), "test", "problems.jl"))
+include(joinpath(@__DIR__, "..", "plotting_utils.jl"))
 
 all_subtypes(::Type{T}) where {T} = isabstracttype(T) ? vcat(all_subtypes.(subtypes(T))...) : [T]
 

src/solvers/ark_algorithm.jl

@@ -383,6 +383,7 @@ function step_u!(integrator, cache::ARKAlgorithmCache)
         # different from the previous state.
         if !isnothing(T_imp!) && !iszero(Δtγ)
             # Solve u′ ≈ u_minus_Δu_imp_from_solve + Δtγ * T_imp(u′, p, t_imp).
+            @. u_on_stage = u # TODO: Is this a good idea?
             solve_newton!(
                 newtons_method,
                 newtons_method_cache,