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October 13, 2025Open Access

A Stiff Order Condition Theory for Runge-Kutta Methods Applied to Semilinear ODEs

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Theoretical framework establishes new order conditions for Runge-Kutta methods in stiff semilinear ODEs, suggesting improved accuracy.

New semilinear order conditions for Runge-Kutta methods prevent order reduction in stiff ODEs, enhancing accuracy.
Conditions are based on orthogonality relations and are enumerated by rooted trees, broadening applicability.
Global error bounds are proven, showing consistency across varying stiffness levels of linear terms.
This approach provides a new perspective on convergence theory for a broader class of ordinary differential equations.

Roberts et al. (2025) studied this question.

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