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Add sixth-order ExpRK6s16 solver - #4893

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Jayant-kernel:feat/exprk6s16
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Jayant-kernel:feat/exprk6s16

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@Jayant-kernel

@Jayant-kernel Jayant-kernel commented Oct 20, 2026 •

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Adds ExpRK6s16, the sixth-order stiff exponential Runge–Kutta method from Luan and Alhsmy, with cached-operator and Krylov support.

Includes convergence coverage for both in-place and out-of-place problems, plus the reaction-diffusion problem from the paper's Example 5.1.

Tested the OrdinaryDiffEqExponentialRK Core group with GROUP=Core julia --project -e 'using Pkg; Pkg.test()' from lib/OrdinaryDiffEqExponentialRK: 179 passed, 4 marked broken.

Closes #2063.

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@ranocha Look at the changes when you are free

@ranocha

ranocha commented Oct 21, 2026

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@ChrisRackauckas (or @ChrisRackauckas-Claude?) are better reviewers for this PR.

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New sixth-order exponential Runge-Kutta methods for parabolic PDEs

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