Add Verner RKV76.IIa 7/6 Runge-Kutta method

[ChrisRackauckas]

Summary

• Implements Verner's RKV76.IIa method, the most efficient 10-stage conventional Runge-Kutta pair of orders 6 and 7
• Adds tableau coefficients from Verner's 2024 update with improved accuracy
• Includes full support for lazy interpolation and comprehensive test coverage

Implementation Details

This PR adds the RKV76.IIa method to the OrdinaryDiffEqVerner package. The implementation includes:

• Algorithm definition with lazy interpolation support
• Complete Butcher tableau with coefficients parsed from Verner's data
• Cache structures for both mutable and constant cache types
• Specialized perform_step! methods
• Interpolation functions for dense output
• Comprehensive tests verifying convergence order

Test Plan

• Tests pass for scalar and system ODEs
• Convergence order verified to be 7
• Lazy and non-lazy interpolation modes tested
• CI tests pass

Fixes #2621

🤖 Generated with Claude Code

[github-actions]

Benchmark Results (Julia v1)

Time benchmarks

	master	2243693...	master / 2243693...
construction/linear_N50	28.2 ± 14 μs	28.5 ± 10 μs	0.988 ± 0.6
construction/lotka_volterra	19.1 ± 0.33 μs	19 ± 0.27 μs	1 ± 0.022
construction/rober	18.9 ± 0.2 μs	19 ± 0.21 μs	0.997 ± 0.015
nonstiff/fitzhugh_nagumo/BS3	0.147 ± 0.011 ms	0.146 ± 0.0099 ms	1.01 ± 0.1
nonstiff/fitzhugh_nagumo/DP5	0.0973 ± 0.0097 ms	0.104 ± 0.0098 ms	0.939 ± 0.13
nonstiff/fitzhugh_nagumo/Tsit5	0.115 ± 0.009 ms	0.127 ± 0.009 ms	0.907 ± 0.095
nonstiff/fitzhugh_nagumo/Vern6	0.17 ± 0.0084 ms	0.175 ± 0.0088 ms	0.971 ± 0.068
nonstiff/fitzhugh_nagumo/Vern7	0.115 ± 0.0088 ms	0.121 ± 0.0088 ms	0.949 ± 0.1
nonstiff/lotka_volterra/BS3	0.292 ± 0.011 ms	0.291 ± 0.011 ms	1 ± 0.054
nonstiff/lotka_volterra/DP5	0.0478 ± 0.018 ms	0.0498 ± 0.016 ms	0.959 ± 0.47
nonstiff/lotka_volterra/Tsit5	0.0626 ± 0.025 ms	0.0669 ± 0.024 ms	0.936 ± 0.5
nonstiff/lotka_volterra/Vern6	0.0827 ± 0.013 ms	0.086 ± 0.011 ms	0.961 ± 0.19
nonstiff/lotka_volterra/Vern7	0.0512 ± 0.022 ms	0.0527 ± 0.022 ms	0.971 ± 0.58
nonstiff/pleiades/BS3	0.088 ± 0.023 s	0.0867 ± 0.016 s	1.02 ± 0.32
nonstiff/pleiades/DP5	1.29 ± 0.098 ms	1.24 ± 0.093 ms	1.04 ± 0.11
nonstiff/pleiades/Tsit5	15.5 ± 6.1 ms	15.5 ± 5.4 ms	0.998 ± 0.52
nonstiff/pleiades/Vern6	7.54 s	6.74 s	1.12
nonstiff/pleiades/Vern7	8.07 s	8.02 s	1.01
scaling/brusselator_2d/16x16	0.3 ± 0.022 s	0.315 ± 0.031 s	0.955 ± 0.12
scaling/brusselator_2d/32x32	7.17 s	7.26 s	0.988
scaling/brusselator_2d/8x8	11.7 ± 0.67 ms	11.2 ± 0.22 ms	1.04 ± 0.063
scaling/linear/N10	0.0373 ± 0.017 ms	0.0392 ± 0.017 ms	0.953 ± 0.61
scaling/linear/N100	0.791 ± 0.014 ms	0.801 ± 0.018 ms	0.988 ± 0.029
scaling/linear/N50	0.212 ± 0.011 ms	0.224 ± 0.011 ms	0.949 ± 0.068
stiff/pollution/FBDF	0.59 ± 0.014 ms	0.594 ± 0.015 ms	0.993 ± 0.034
stiff/pollution/KenCarp4	0.549 ± 0.0099 ms	0.549 ± 0.01 ms	1 ± 0.026
stiff/pollution/Rodas4	0.767 ± 0.019 ms	0.767 ± 0.018 ms	1 ± 0.034
stiff/pollution/Rosenbrock23	1.34 ± 0.038 ms	1.35 ± 0.037 ms	0.995 ± 0.039
stiff/pollution/TRBDF2	0.511 ± 0.012 ms	0.516 ± 0.011 ms	0.991 ± 0.031
stiff/rober/FBDF	0.608 ± 0.01 ms	0.618 ± 0.01 ms	0.985 ± 0.023
stiff/rober/KenCarp4	0.769 ± 0.019 ms	0.768 ± 0.02 ms	1 ± 0.036
stiff/rober/Rodas4	0.419 ± 0.0094 ms	0.41 ± 0.011 ms	1.02 ± 0.035
stiff/rober/Rosenbrock23	0.284 ± 0.0094 ms	0.278 ± 0.0094 ms	1.02 ± 0.048
stiff/rober/TRBDF2	1.75 ± 0.014 ms	1.79 ± 0.013 ms	0.976 ± 0.011
stiff/van_der_pol/FBDF	9.93 ± 0.09 ms	9.99 ± 0.075 ms	0.994 ± 0.012
stiff/van_der_pol/KenCarp4	4.83 ± 0.067 ms	4.96 ± 0.063 ms	0.974 ± 0.018
stiff/van_der_pol/Rodas4	7.43 ± 0.066 ms	7.48 ± 0.039 ms	0.994 ± 0.01
stiff/van_der_pol/Rosenbrock23	21.4 ± 0.24 ms	21.1 ± 0.2 ms	1.01 ± 0.015
stiff/van_der_pol/TRBDF2	3.07 ± 0.092 ms	3.09 ± 0.091 ms	0.993 ± 0.042
time_to_load	3.23 ± 0.0086 s	3.22 ± 0.026 s	1 ± 0.0084

Memory benchmarks

	master	2243693...	master / 2243693...
construction/linear_N50	0.071 k allocs: 0.0411 MB	0.071 k allocs: 0.0411 MB	1
construction/lotka_volterra	0.065 k allocs: 2.45 kB	0.065 k allocs: 2.45 kB	1
construction/rober	0.065 k allocs: 2.42 kB	0.065 k allocs: 2.42 kB	1
nonstiff/fitzhugh_nagumo/BS3	3.69 k allocs: 0.164 MB	3.69 k allocs: 0.164 MB	1
nonstiff/fitzhugh_nagumo/DP5	2.63 k allocs: 0.127 MB	2.63 k allocs: 0.127 MB	1
nonstiff/fitzhugh_nagumo/Tsit5	4 k allocs: 0.182 MB	4 k allocs: 0.182 MB	1
nonstiff/fitzhugh_nagumo/Vern6	4.54 k allocs: 0.207 MB	4.54 k allocs: 0.207 MB	1
nonstiff/fitzhugh_nagumo/Vern7	3.91 k allocs: 0.165 MB	3.91 k allocs: 0.165 MB	1
nonstiff/lotka_volterra/BS3	7.88 k allocs: 0.365 MB	7.88 k allocs: 0.365 MB	1
nonstiff/lotka_volterra/DP5	1.21 k allocs: 0.0543 MB	1.21 k allocs: 0.0543 MB	1
nonstiff/lotka_volterra/Tsit5	2.17 k allocs: 0.093 MB	2.17 k allocs: 0.093 MB	1
nonstiff/lotka_volterra/Vern6	2.24 k allocs: 0.0986 MB	2.24 k allocs: 0.0986 MB	1
nonstiff/lotka_volterra/Vern7	1.65 k allocs: 0.0736 MB	1.65 k allocs: 0.0736 MB	1
nonstiff/pleiades/BS3	0.685 M allocs: 0.0675 GB	0.685 M allocs: 0.0675 GB	1
nonstiff/pleiades/DP5	6.63 k allocs: 0.51 MB	6.63 k allocs: 0.51 MB	1
nonstiff/pleiades/Tsit5	0.186 M allocs: 20.4 MB	0.186 M allocs: 20.4 MB	1
nonstiff/pleiades/Vern6	0.038 G allocs: 4.05 GB	0.038 G allocs: 4.05 GB	1
nonstiff/pleiades/Vern7	0.044 G allocs: 4.63 GB	0.044 G allocs: 4.63 GB	1
scaling/brusselator_2d/16x16	3.58 k allocs: 0.152 GB	3.58 k allocs: 0.152 GB	1
scaling/brusselator_2d/32x32	3.4 k allocs: 2.22 GB	3.4 k allocs: 2.22 GB	1
scaling/brusselator_2d/8x8	2.62 k allocs: 8.76 MB	2.62 k allocs: 8.76 MB	1
scaling/linear/N10	0.752 k allocs: 0.0514 MB	0.752 k allocs: 0.0514 MB	1
scaling/linear/N100	2.27 k allocs: 0.901 MB	2.27 k allocs: 0.901 MB	1
scaling/linear/N50	1.66 k allocs: 0.348 MB	1.66 k allocs: 0.348 MB	1
stiff/pollution/FBDF	1.5 k allocs: 0.288 MB	1.5 k allocs: 0.288 MB	1
stiff/pollution/KenCarp4	0.516 k allocs: 0.134 MB	0.516 k allocs: 0.134 MB	1
stiff/pollution/Rodas4	1.28 k allocs: 0.363 MB	1.28 k allocs: 0.363 MB	1
stiff/pollution/Rosenbrock23	2.77 k allocs: 0.819 MB	2.77 k allocs: 0.819 MB	1
stiff/pollution/TRBDF2	0.783 k allocs: 0.168 MB	0.783 k allocs: 0.168 MB	1
stiff/rober/FBDF	2.89 k allocs: 0.137 MB	2.89 k allocs: 0.137 MB	1
stiff/rober/KenCarp4	1.3 k allocs: 0.0575 MB	1.3 k allocs: 0.0575 MB	1
stiff/rober/Rodas4	2.19 k allocs: 0.106 MB	2.19 k allocs: 0.106 MB	1
stiff/rober/Rosenbrock23	2.51 k allocs: 0.117 MB	2.51 k allocs: 0.117 MB	1
stiff/rober/TRBDF2	7.72 k allocs: 0.36 MB	7.72 k allocs: 0.36 MB	1
stiff/van_der_pol/FBDF	0.0444 M allocs: 2.2 MB	0.0444 M allocs: 2.2 MB	1
stiff/van_der_pol/KenCarp4	4.27 k allocs: 0.184 MB	4.27 k allocs: 0.184 MB	1
stiff/van_der_pol/Rodas4	0.0377 M allocs: 1.86 MB	0.0377 M allocs: 1.86 MB	1
stiff/van_der_pol/Rosenbrock23	0.213 M allocs: 9.09 MB	0.213 M allocs: 9.09 MB	1
stiff/van_der_pol/TRBDF2	5.02 k allocs: 0.212 MB	5.02 k allocs: 0.212 MB	1
time_to_load	0.159 k allocs: 11.2 kB	0.159 k allocs: 11.2 kB	1