Tableau Implementation for Tsit5 #2913

KeshavVenkatesh · 2025-11-24T01:15:12Z

In this PR, I have attempted to implement the butcher tableau approach for the Tsit5 algorithm for both solving and interpolation.

I have used the coefficient values from OrdinaryDiffEqExplicitRK. I am working on extending the benchmark tests for interpolation.

Please review my changes and provide feedback for the following:

On the implementation for solving and interpolation.
The logic for benchmark tests, results and suggestions on how I can improve them. Are the numerical differences in values between two approaches acceptable?
Suggestions for how I can extend the benchmark tests for interpolations as well.

KeshavVenkatesh · 2025-12-02T03:05:13Z

@ChrisRackauckas : Request you to kindly review this PR and provide your feedback

oscardssmith · 2025-12-02T15:50:47Z

lib/OrdinaryDiffEqExplicitRK/src/explicit_rk_interp.jl

+"""
+Evaluate a polynomial at Θ, given coefficients for Θ¹, Θ², ..., Θ⁶.
+Assumes coeffs = [a₁, a₂, ..., a₆] for Θ¹, Θ², ..., Θ⁶.
+"""
+function eval_poly_theta(Θ, coeffs)
+    # coeffs[1]*Θ + coeffs[2]*Θ^2 + ... + coeffs[6]*Θ^6
+    return sum(coeffs[i] * Θ^i for i in 1:length(coeffs))
+end


isn't this just evalpoly?

KeshavVenkatesh · 2025-12-03T15:37:02Z

lib/OrdinaryDiffEqExplicitRK/src/explicit_rk_interp.jl

+        [@evalpoly(Θ, tableau[i,:]...) for i in 1:num_stages]
+    else
+        # For derivative: d/dΘ [a₀ + a₁*Θ + a₂*Θ² + ...] = a₁ + 2*a₂*Θ + 3*a₃*Θ² + ...
+        [@evalpoly(Θ, [j * tableau[i, j+1] for j in 1:(num_coeffs-1)]...) for i in 1:num_stages]


@oscardssmith : Thanks for the feedback and suggestion. Apologies I was not familiar with this. Could you please check if this change looks right?

ChrisRackauckas · 2025-12-17T04:35:53Z

Sorry was trying to get this repo passing tests again first.

This should just be added as part of the normal ExplicitRK implementation. With a field for the interpolation values added to the ExplicitRKTableau definition in DiffEqBase.

Note this is the same tableau as the one that is tested https://github.com/SciML/DiffEqDevTools.jl/blob/master/src/ode_tableaus.jl#L989

KeshavVenkatesh · 2025-12-17T06:22:48Z

Thank you for these updates. I will work on what you said and send you a new PR tomorrow.

KeshavVenkatesh · 2025-12-18T05:57:11Z

@ChrisRackauckas Could you please review the changes I have made? I will do some more testing, but I wanted to know if I have incorporated your suggestions. I have also created a new PR in DiffEqBase, can you please review that as well? Thanks!

ChrisRackauckas · 2025-12-18T10:39:31Z

all of the generic_dense parts are missing?

KeshavVenkatesh · 2025-12-19T07:14:17Z

all of the generic_dense parts are missing?

@ChrisRackauckas Does this involve implementing equivalent logic as in

OrdinaryDiffEq.jl/lib/OrdinaryDiffEqTsit5/src/interpolants.jl

Line 38 in 0fb3a7e

    
           @muladd function _ode_interpolant(Θ, dt, y₀, y₁, k, cache::Tsit5ConstantCache,

ChrisRackauckas · 2025-12-19T07:17:24Z

Yes exactly, just for the ExplicitRK tableau with its generic coefficient vector.

KeshavVenkatesh · 2025-12-21T20:52:32Z

Yes exactly, just for the ExplicitRK tableau with its generic coefficient vector.

@ChrisRackauckas Could you please review this PR and provide your feedback? I have implemented this based on my understanding of how it was implemented for Tsit5 in this code here, but I made it generic for different orders.

ChrisRackauckas · 2025-12-29T13:55:21Z

lib/OrdinaryDiffEqExplicitRK/src/algorithms.jl

+function construct_tsit5_interp_matrix_auto(T::Type)
+    if T <: Union{Float32, Float64}
+        return construct_tsit5_interp_matrix(T)
+    else
+        return construct_tsit5_interp_matrix_highprecision(T)


this hsould just be dispatch

ChrisRackauckas · 2025-12-29T13:55:30Z

lib/OrdinaryDiffEqExplicitRK/src/algorithms.jl

+
+Automatically selects appropriate precision based on type.
+"""
+function construct_tsit5_interp_matrix_auto(T::Type)


Suggested change

function construct_tsit5_interp_matrix_auto(T::Type)

function construct_tsit5_interp_matrix_auto(::Type{T}) where T

force specialize

ChrisRackauckas · 2025-12-29T13:55:46Z

lib/OrdinaryDiffEqExplicitRK/src/algorithms.jl

+High-precision version for BigFloat and other arbitrary-precision types.
+We have not tested this
+"""
+function construct_tsit5_interp_matrix_highprecision(T::Type)


Suggested change

function construct_tsit5_interp_matrix_highprecision(T::Type)

function construct_tsit5_interp_matrix_highprecision(::Type{T}) where T

ChrisRackauckas · 2025-12-29T13:56:11Z

lib/OrdinaryDiffEqExplicitRK/src/algorithms.jl

+    ... and so on for all 7 stages
+=
+"""
+function construct_tsit5_interp_matrix(T::Type = Float64)


Suggested change

function construct_tsit5_interp_matrix(T::Type = Float64)

function construct_tsit5_interp_matrix(::Type{Float64})

ChrisRackauckas · 2025-12-29T13:57:33Z

lib/OrdinaryDiffEqExplicitRK/src/explicit_rk_perform_step.jl

+end
+
+# In-place version
+function generic_rk_interpolant!(out, Θ, dt, y₀, k, B_interp; idxs=nothing, order=0)


these aren't implementing the dense.jl dispatches required for the interpolation to be used in the solution. Check OrdinaryDiffEqCore/src/dense. See how it's done for example with OrdinaryDiffEqVerner.

ChrisRackauckas · 2025-12-29T13:58:14Z

Sorry got behind having to revive a bit of this repo. Left some comments. Still some work to do here but on the right track

KeshavVenkatesh · 2026-01-03T23:31:11Z

@ChrisRackauckas In the latest PR, I have incorporated the logic for dense interpolation and also addressed your comments on force specialization and dispatch support.

I will now work on benchmarking and functional tests for these changes.

KeshavVenkatesh · 2026-01-07T01:25:40Z

@ChrisRackauckas Could you please review this pull request?

KeshavVenkatesh · 2026-01-16T02:57:01Z

Could you please review the pull request that I sent a link to? Thanks!

ChrisRackauckas · 2026-01-16T04:23:28Z

That looks right. Is that PR not to here?

KeshavVenkatesh · 2026-01-16T04:42:37Z

Yes, it is. Is the PR ready to be merged?

ChrisRackauckas · 2026-01-16T04:49:23Z

if tests are passing. needs a rebase and then those changes and yeah it looks like that makes it ready

KeshavVenkatesh · 2026-01-16T19:06:37Z

if tests are passing. needs a rebase and then those changes and yeah it looks like that makes it ready

@ChrisRackauckas, thanks for your feedback. I will work on rebasing the PR, running the test, and getting the PR ready for landing.

Is there anything I can work on in parallel? I have a (slightly) better understanding of the codebase from the work I have done so far, and I would love to pick up any medium/large work to get a better understanding and contribute more.

Also if you have any feedback on my work so far - specifically on what I can improve - I would greatly appreciate it.

I also wanted to say that this work is really interesting and wanted to thank you for the opportunity you provided.

Tableau Implementation for Tsit5

e2babc8

oscardssmith reviewed Dec 2, 2025

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Using builtin eval-poly

4c7e171

KeshavVenkatesh commented Dec 3, 2025

View reviewed changes

Refactored code

8f598df

Generic interpolant for ExplicitRK

3febbb5

ChrisRackauckas reviewed Dec 29, 2025

View reviewed changes

generic interpolant implementation and code cleanup for dispatch

1cfe30f

	function construct_tsit5_interp_matrix_auto(T::Type)
	function construct_tsit5_interp_matrix_auto(::Type{T}) where T

	function construct_tsit5_interp_matrix_highprecision(T::Type)
	function construct_tsit5_interp_matrix_highprecision(::Type{T}) where T

	function construct_tsit5_interp_matrix(T::Type = Float64)
	function construct_tsit5_interp_matrix(::Type{Float64})

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Tableau Implementation for Tsit5 #2913

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Tableau Implementation for Tsit5 #2913

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