Add Cash-Karp 5th order Runge-Kutta method #2771
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Implements the classic Cash-Karp 5/4 embedded Runge-Kutta method: - 6-stage explicit method with 5th order accuracy - Embedded 4th order method for error estimation - Adaptive step size control - Both constant and mutable cache implementations Added components: - CashKarp5 algorithm struct in algorithms.jl - CashKarp5ConstantCache tableau with rational and float coefficients - CashKarp5Cache mutable cache structure - perform_step! methods for both cache types - initialize! methods for proper integration setup - Convergence test to verify 5th order accuracy - Export in module interface The method provides an alternative to DP5 and BS5 for applications requiring 5th order accuracy with different stability properties. References: Cash, J.R. and Karp, A.H. (1990). A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software, 16(2), 201-222. 🤖 Generated with [Claude Code](https://claude.ai/code) Co-Authored-By: Claude <[email protected]>
Benchmark Results (Julia v1)Time benchmarks
Memory benchmarks
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- Add get_fsalfirstlast method for CashKarp5Cache - Mark CashKarp5 as non-FSAL algorithm via isfsal trait This fixes the MethodError that occurred when initializing the integrator. Even though CashKarp5 is not FSAL, the get_fsalfirstlast method is still required by the integrator initialization process. 🤖 Generated with [Claude Code](https://claude.ai/code) Co-Authored-By: Claude <[email protected]>
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Summary
Implements the classic Cash-Karp 5/4 embedded Runge-Kutta method, adding a well-known 5th order method that was previously missing from OrdinaryDiffEq.jl.
Changes
Method Details
Test Plan
Background
The Cash-Karp method was identified as missing from OrdinaryDiffEq.jl based on discussions about classical RK methods. While DP5 and BS5 provide similar functionality, Cash-Karp offers different stability properties and is widely referenced in numerical analysis literature.
References
Cash, J.R. and Karp, A.H. (1990). A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software, 16(2), 201-222.
🤖 Generated with Claude Code