Adding Alshina2, Alshina3, Alshin6 from Alshina, Zaks, and Kalitkin (2008) #1898

ayushinav · 2023-03-10T21:09:43Z

Adding the 2nd order from Alshina, Zaks, and Kalitkin (2008), Optimal first- to sixth-order accurate Runge-Kutta schemes.
This is not a new algo per se (trying to get familiar with the code structure), but if it works fine, I'll add the other orders soon.

ErikQQY

Here are some suggestions:

Please make sure the new scheme passes the convergence tests to ensure the implementation is correct, for example, you can put this new scheme in a self-contained example to easily test the implementation. Also, you can learn from existing schemes or merged PRs to get familiar with the structure.
Add convergence plots so that it would be convenient for committers to be sure this new scheme "behaves" well, see devdocs about the convergence plots.
Since all of the SciML projects follow the SciML style, it would be nice if you can format your commit before pushing, see the CONTRIBUTING.md to know how.

ayushinav · 2023-03-14T07:41:31Z

Thanks for the suggestions, @ErikQQY. Updated the codes and added the other methods.

ErikQQY · 2023-03-15T02:20:02Z

src/algorithms.jl

+  step_limiter!::StepLimiter
+  thread::Thread
+end
+export Alshina2


Since we already export this algorithm in the OrdinaryDiffEq.jl file, this export is redundant.

ErikQQY · 2023-03-15T02:20:13Z

src/algorithms.jl

+  step_limiter!::StepLimiter
+  thread::Thread
+end
+export Alshina3


ErikQQY · 2023-03-15T02:20:18Z

src/algorithms.jl

+  step_limiter!::StepLimiter
+  thread::Thread
+end
+export Alshina4


ErikQQY · 2023-03-15T02:20:27Z

src/algorithms.jl

+  step_limiter!::StepLimiter
+  thread::Thread
+end
+export Alshina6


ErikQQY · 2023-03-15T02:26:17Z

test/algconvergence/ode_convergence_tests.jl

+
+    sim6 = test_convergence(dts1, prob, Alshina6())
+    @test sim6.𝒪est[:l2]≈4 atol=testTol
+


The convergence tests here look weird. What we are doing here is testing whether the order of the convergence estimate is equal to the order of this method. If it doesn't equal, you can adjust dts so that it doesn't saturate, if it still doesn't converge, then there are bugs in your implementation, you need to carefully compare your implementation with this paper, probably some coefficients or the initialize! and perform_step! are wrong.

Right, my implementation had bugs. I was so confused by FSAL being used inspite of the algorithm not being FSAL'd. It's clear to me now.

The convergence tests make so much sense now. Also, am I correct in understanding that integrator.stats.nf stores the number of function calls?

ChrisRackauckas · 2023-03-16T09:53:15Z

src/tableaus/low_order_rk_tableaus.jl

+struct Alshina4ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache
+    a21::T
+    a31::T
+    a32::T
+    a41::T
+    a42::T
+    a43::T
+
+
+    b1::T
+    b2::T
+    b3::T
+    b4::T
+
+    c2::T2
+    c3::T2
+    c4::T2
+
+end
+
+function Alshina4ConstantCache(T::Type{<:Float64}, T2::Type{<:Float64})
+    a21 = convert(T, 0.5)
+    a31 = convert(T, 0.0)
+    a32 = convert(T, 0.5)
+    a41 = convert(T, 0.0)
+    a42 = convert(T, 0.0)
+    a43 = convert(T, 1.0)
+
+    b1 = convert(T, 0.16666666666666666)
+    b2 = convert(T, 0.3333333333333333)
+    b3 = convert(T, 0.3333333333333333)
+    b4 = convert(T, 0.16666666666666666)
+
+    c2 = convert(T2, 0.5)
+    c3 = convert(T2, 0.5)
+    c4 = convert(T2, 1.0)
+
+    Alshina4ConstantCache(a21, a31, a32, a41, a42, a43, b1, b2, b3, b4, c2, c3, c4)
+end


This is just RK4?

Do I need to resolve anything here? This is indeed just RK4.

Delete it because it's not useful.

ChrisRackauckas · 2023-03-16T09:58:12Z

src/tableaus/low_order_rk_tableaus.jl

+function Alshina2ConstantCache(T::Type{<:Float64}, T2::Type{<:Float64})
+    a21 = convert(T, 0.6666666666666666)
+
+    b1 = convert(T, 0.25)
+    b2 = convert(T, 0.75)
+
+    c2 = convert(T2, 0.6666666666666666)
+
+    Alshina2ConstantCache(a21, b1, b2, c2)


the non float64 dispatches are missing

ChrisRackauckas · 2023-03-16T09:58:40Z

src/tableaus/low_order_rk_tableaus.jl

+
+function Alshina3ConstantCache(T::Type{<:Float64}, T2::Type{<:Float64})
+    a21 = convert(T, 0.5)
+    a31 = convert(T, 0.0)


remove the zeros from the calculation

ChrisRackauckas · 2023-03-16T10:11:22Z

src/tableaus/low_order_rk_tableaus.jl

+    b3 = convert(T, 0.3333333333333333)
+    b4 = convert(T, 0.16666666666666666)
+


Embedded schemes are missing?

Ahh, I guess I did not include them because the paper had only for RK2 and RK3. My bad, will include them shortly.

ayushinav · 2023-03-18T02:58:25Z

Updated

ayushinav · 2023-03-21T00:05:32Z

Also, I guess there's a small bug in here, utilde is not brought in. I get the utilde not defined error when I run the in place lorenz fn using SIR54().

ayushinav · 2023-03-21T23:11:03Z

Added the regression tests as I understood. Please let me know if anything needs to be changed.

prob_linear= ODEProblemLibrary.prob_ode_linear

function lorenz!(du,u,p,t)
    du[1] = 10.0(u[2]-u[1])
    du[2] = u[1]*(28.0-u[3]) - u[2]
    du[3] = u[1]*u[2] - (8/3)*u[3]
end
u0 = [1.0;0.0;0.0]
tspan = (0.0,1.0)
prob_lorenz = ODEProblem(lorenz!,u0,tspan)

sol_linear2 = solve(prob_linear, Alshina2())
@show length(sol_linear2.u)

sol_lorenz2 = solve(prob_lorenz,Alshina2())
@show length(sol_lorenz2.t)

sol_linear3 = solve(prob_linear, Alshina3())
@show length(sol_linear3.u)

sol_lorenz3 = solve(prob_lorenz,Alshina3())
@show length(sol_lorenz3.t)

gives

length(sol_linear2.u) = 2040
length(sol_lorenz2.t) = 64110
length(sol_linear3.u) = 1286
length(sol_lorenz3.t) = 40524

ChrisRackauckas · 2023-03-22T18:13:50Z

Test failure looks real.

ayushinav · 2023-03-22T20:56:03Z

I was not clear what the failures meant. Made the changes. Hope it looks right now.

ChrisRackauckas · 2023-03-24T13:44:12Z

test/regression/ode_adaptive_tests.jl

+function lorenz!(du,u,p,t)
+    du[1] = 10.0(u[2]-u[1])
+    du[2] = u[1]*(28.0-u[3]) - u[2]
+    du[3] = u[1]*u[2] - (8/3)*u[3]
+end
+u0 = [1.0;0.0;0.0]
+tspan = (0.0,1.0)
+prob_lorenz = ODEProblem(lorenz!,u0,tspan)


already defined above

True. The same function is defined on line 33. While I was trying to understand the tests, I realized that ESDIRK tests use the lorenz defined on line 59, which does not update the du and will always give 8 as the length of the soln, irrespective of the adaptive method used. Though ESDIRK pass the tests on right lorenz too, I did it to explicitly show what's happening.

test/regression/ode_adaptive_tests.jl

ChrisRackauckas · 2023-03-24T14:30:33Z

test/regression/ode_adaptive_tests.jl

+
+sol_linear = solve(prob_linear, Alshina2())
+sol_lorenz = solve(prob_lorenz, Alshina2())
+@test length(sol_linear.u) < length(sol_lorenz.u)


I'm not sure this relative test makes sense.

I am not entirely surely sure about what to put in. Could you please point to what exactly I might be putting in? Thanks

Make it a regression test like the ones on linear above.

Would this be fine then?

for prob in [prob_ode_2Dlinear, prob_ode_linear] sol = solve(prob, Alshina2()) val= maximum(abs.(sol.u[end] - sol.u_analytic[end])) @test val<1e-6 sol = solve(prob, Alshina3()) val= maximum(abs.(sol.u[end] - sol.u_analytic[end])) @test val<1e-6 end

ChrisRackauckas · 2023-03-26T07:16:20Z

Rebase onto master.

ayushinav · 2023-03-30T22:58:53Z

Rebased again. Please let me know if I have to make any changes in here.

ErikQQY · 2023-04-02T14:10:46Z

After adding these algorithms, it would be nice if you can record these new methods in solvers docs: DiffEqDocs.jl @ayushinav

ayushinav and others added 6 commits March 10, 2023 14:52

Adding ERKO2

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ayushinav closed this Mar 11, 2023

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ayushinav marked this pull request as draft March 11, 2023 00:39

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Added Alshina2, Alshina3, Alshina4, Alshina6 methods

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ayushinav marked this pull request as ready for review March 14, 2023 07:39

ayushinav requested a review from ErikQQY March 14, 2023 19:48

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ayushinav force-pushed the master branch from 1122498 to 21df5b0 Compare March 18, 2023 02:09

ayushinav added 3 commits March 17, 2023 22:11

removed Alshina4, added embedded methods and bug fixes

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Merge branch 'master' of https://github.com/ayushinav/OrdinaryDiffEq.jl

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ayushinav changed the title ~~2nd order of Alshina, Zaks, and Kalitkin (2008)~~ Adding Alshina2, Alshina3, Alshin6 from Alshina, Zaks, and Kalitkin (2008) Mar 23, 2023

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ErikQQY mentioned this pull request Apr 5, 2023

Add docs for SIR54, CG4a and Alshina methods SciML/DiffEqDocs.jl#668

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Adding Alshina2, Alshina3, Alshin6 from Alshina, Zaks, and Kalitkin (2008) #1898

Adding Alshina2, Alshina3, Alshin6 from Alshina, Zaks, and Kalitkin (2008) #1898

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		sim6 = test_convergence(dts1, prob, Alshina6())
		@test sim6.𝒪est[:l2]≈4 atol=testTol

		b3 = convert(T, 0.3333333333333333)
		b4 = convert(T, 0.16666666666666666)

Adding Alshina2, Alshina3, Alshin6 from Alshina, Zaks, and Kalitkin (2008) #1898

Adding Alshina2, Alshina3, Alshin6 from Alshina, Zaks, and Kalitkin (2008) #1898

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