Fix SplitFunction to use user-provided jvp function

[ChrisRackauckas-Claude]

Summary

This PR fixes issue SciML/DifferentialEquations.jl#1109 where SplitFunction was not using user-provided jvp (Jacobian-vector product) functions even when supplied.

Problem

When a user provides a jvp function to SplitFunction, it should be used instead of falling back to automatic differentiation. However, the has_jvp check for SplitFunction was only checking f.f1 instead of first checking the SplitFunction's own jvp field.

# Old behavior
has_jvp(f::Union{SplitFunction, SplitSDEFunction}) = has_jvp(f.f1)

This caused the solver to use ForwardDiff with Dual numbers even when an analytical jvp was provided, leading to MethodErrors when the function signatures were restricted to Vector{Float64}.

Solution

Modified the has_* functions for SplitFunction and SplitSDEFunction to check their own fields first before delegating to f.f1. This allows user-provided analytical derivatives (jvp, vjp, jac, tgrad, Wfact, etc.) to be properly detected and used with matrix-free Krylov solvers.

# New behavior
function has_jvp(f::Union{SplitFunction, SplitSDEFunction})
    (__has_jvp(f) && f.jvp !== nothing) || has_jvp(f.f1)
end

Testing

• ✅ All existing SciMLBase tests pass
• ✅ Tested with the MRE from the issue - now works without errors
• ✅ Code formatted with JuliaFormatter using SciMLStyle

Related Issue

Fixes SciML/DifferentialEquations.jl#1109

🤖 Generated with Claude Code

Co-Authored-By: Claude [email protected]