Move BVP default solver from DifferentialEquations.jl to BoundaryValueDiffEq.jl

[ChrisRackauckas-Claude]

Summary

• Moves the default solver for BVP problems from DifferentialEquations.jl to BoundaryValueDiffEq.jl
• Adds default __init and __solve methods for BVProblem that use Shooting(Tsit5())
• Updates Aqua tests to properly handle the type-piracy for these new default methods

Changes

1. Added OrdinaryDiffEqTsit5 as a dependency to provide the Tsit5 algorithm
2. Implemented SciMLBase.__init and SciMLBase.__solve methods for BVProblem in the main module
3. Updated Aqua tests to mark BVProblem as "owned" for type-piracy checking
4. Added test for default solver functionality

Related

This PR builds on the work from #370 but targets the master branch and properly handles the Aqua test updates.

Test plan

• Tests pass locally
• Default solver works when no algorithm is specified
• Aqua tests pass with the type-piracy properly marked

🤖 Generated with Claude Code

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Benchmark Results

Click to check benchmark results

	master	718f3b5...	master / 718f3b5...
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK2()	0.585 ± 0.018 s	0.581 ± 0.015 s	1.01 ± 0.04
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK3()	13.7 ± 0.55 ms	13.6 ± 0.61 ms	1 ± 0.06
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK4()	3.12 ± 0.16 ms	3.12 ± 0.19 ms	1 ± 0.08
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK5()	9.3 ± 1.2 ms	9.29 ± 1.3 ms	1 ± 0.19
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK6()	1.62 ± 0.29 ms	1.61 ± 0.27 ms	1 ± 0.25
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = false)	1.84 ± 0.65 ms	1.84 ± 0.65 ms	0.999 ± 0.5
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = true)	3.1 ± 0.99 ms	3.1 ± 0.96 ms	0.998 ± 0.45
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.0664 ± 0.0066 s	0.0667 ± 0.0067 s	0.995 ± 0.14
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.0796 ± 0.0069 s	0.0805 ± 0.0069 s	0.989 ± 0.12
Simple Pendulum/IIP/Shooting(Tsit5())	0.234 ± 0.074 ms	0.239 ± 0.076 ms	0.981 ± 0.44
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK2()	0.736 ± 0.0057 s	0.729 ± 0.01 s	1.01 ± 0.016
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK3()	16.5 ± 5.5 ms	16.7 ± 5.6 ms	0.989 ± 0.47
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK4()	3.59 ± 0.12 ms	3.59 ± 0.17 ms	1 ± 0.058
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK5()	10.8 ± 1.7 ms	10.8 ± 1.8 ms	1 ± 0.23
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK6()	1.87 ± 0.13 ms	1.87 ± 0.14 ms	0.997 ± 0.1
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = false)	3.57 ± 2.9 ms	3.55 ± 2.9 ms	1.01 ± 1.2
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = true)	6.2 ± 5.1 ms	6.04 ± 4.9 ms	1.03 ± 1.2
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.115 ± 0.0028 s	0.118 ± 0.0035 s	0.98 ± 0.037
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.141 ± 0.0046 s	0.143 ± 0.006 s	0.985 ± 0.052
Simple Pendulum/OOP/Shooting(Tsit5())	0.628 ± 0.033 ms	0.625 ± 0.036 ms	1 ± 0.078
time_to_load	5.36 ± 0.0036 s	5.49 ± 0.032 s	0.977 ± 0.0057

### Benchmark Plots A plot of the benchmark results has been uploaded as an artifact to the workflow run for this PR. Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).