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This is a Quantitative Study study.

September 24, 2025Open Access

Automated Runge-Kutta-Nyström time stepping for finite element methods in Irksome

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Updates to Irksome automate Runge-Kutta-Nyström methods for PDE solving, suggesting advantages in performance.

Runge-Kutta-Nyström methods improve efficiency in solving complex wave equations and systems of mixed temporal order.
Numerical results demonstrate competitiveness of fully implicit Runge-Kutta-Nyström methods compared to traditional approaches.
Utilizing an interface closer to problem formulations in UFL leads to reduced algebraic system sizes and runtime.
Effective preconditioning is essential for optimizing performance in dynamic poroelasticity applications.

Kirby et al. (2025) studied this question.

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