Tableau Implementation for Tsit5 #2913
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@ChrisRackauckas : Request you to kindly review this PR and provide your feedback |
oscardssmith
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Dec 2, 2025
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| """ | ||
| 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 |
KeshavVenkatesh
commented
Dec 3, 2025
| [@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] |
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@oscardssmith : Thanks for the feedback and suggestion. Apologies I was not familiar with this. Could you please check if this change looks right?
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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: